If f is analytic and never zero on a domain D, then the graph (x,y,|f(x+iy)|) has no "pits". This follows from the fact that Re(f(z)) has no local minima in D.
Exercise 15 establishes the following result: if f is analytic and never zero on a domain D, then the the real part of f(z) has no local minima in D.
To use this result to establish the statement that |f(z)| has no local minima in D, we can use the fact that[tex]|f(z)|=\sqrt{real part of f(z))^2 + \ img part of f(z) )^2[/tex] . Since the sum of two non-negative functions is non-negative, it follows that if the real part of f(z) has no local minima in D, then |f(z)| has no local minima in D either.
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Estimate the maximum fuel cell area that can be operated at 1 A/cmunder the condition from Example 5.2.Assume a stoichiometric number of 2.Assume that the fuel cell is made of a single straight flow channel. Discuss why channel flow in fuel cells is almost always considered to be laminar
The maximum fuel cell area that can be operated at 1 A/cm^2 under the given conditions can be estimated using the equation A = I/(2FJ), where A is the maximum cell area, I is the current density (1 A/cm^2), F is the Faraday constant, and J is the current density per unit area. Assuming a stoichiometric number of 2 and substituting the given values, we get A = 0.029 m^2 or 290 cm^2.
Channel flow in fuel cells is almost always considered to be laminar because turbulent flow can cause mixing of the reactants and products, reducing the efficiency of the fuel cell. Laminar flow allows for efficient mass transport of the reactants and products to and from the electrode surface. Additionally, laminar flow reduces the likelihood of damage to the fuel cell due to erosion or corrosion caused by turbulent flow. However, the design of fuel cell flow channels can also affect the degree of turbulence and mixing, and optimizing this balance is an ongoing area of research.
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You deposit $100 in a savings account. The account earns 8% simple interest per year.
Answer:
124 and 125.97
Step-by-step explanation:
y
Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch.
I need help D:please !!!!
If the top of Bria's bookcase has a length-to-width ratio of 3:1, the width of the top should be about 10 inches to provide an area of 300 square inches for her soap carving collection.
How to find the dimension of the top of the bookcaseThe top of the bookcase is a rectangle, the area of the top can be expressed as the product of its length and width:
Area of the top = length × width
Area of the top = 300 square inches
length × width = 300 square inches
width = 300 square inches / length
Assuming that the top of the bookcase is with a length-to-width ratio of
3 : 1
length = 3 × width
substituting the value gives
width = 300 / (3 × width)
Simplifying, we have:
width² = 100 square inches (the polynomial)
Taking the square root of both sides, we get:
width = √100 ≈ 10 inches
Then the length will be = 30 inches
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X and Y are independent exponential RVs with parameters 1 and 2, respectively. What is the joint CDF of X and Y? OFxy (a,b) = -4e-26, a > 0,6> 0 OFxy (a, b) = 2e-e-2 , a > 0,6 > 0 O Fxy (a,b) = (1 - e-a) (1 - e-26), a > 0, 6 > 0
The joint CDF of X and Y, two independent exponential random variables with parameters 1 and 2, respectively, is Fxy(a,b) = (1 - e^(-a))(1 - e^(-2b)), where a > 0 and b > 0. The correct answer is C).
Since X and Y are independent, the joint CDF of X and Y is the product of their marginal CDFs:
FXY(a,b) = FX(a)FY(b)
where FX and FY are the CDFs of X and Y, respectively.
The CDF of an exponential distribution with parameter λ is given by:
FX(x) = 1 - e^(-λx)
Therefore, the marginal CDFs of X and Y are:
FX(a) = 1 - e^(-a), λ = 1
FY(b) = 1 - e^(-2b), λ = 2
Taking the product, we get:
FXY(a,b) = FX(a)FY(b) = (1 - e^(-a))(1 - e^(-2b))
Therefore, the answer is:
Fxy (a,b) = (1 - e^(-a))(1 - e^(-2b)), a > 0, b > 0.
The correct option is C).
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what is the number of real solutions
X^2+6x=5
Answer options
1. No real solutions
2. Cannot be determined
3. Two real solutions
4. One real solution
In the given situation we know that the equation X²+6x=5 has (3) two real solutions.
What do we mean by real solutions?In algebra, a real solution is just an answer to an equation that is a real number.
Discriminant b² - 4ac has zero value in the case of a single actual solution.
One solution, x = -1, exists for the equation x² + 2x + 1 = 0.
The Determinant Calculator on Cuemath can be used to determine the determinant of a quadratic equation.
Use the formula: b²-4ac
Insert values:
b²-4ac
6²-4(1)(5)
36-20
16
We know that:
If b²-4ac is > o (Two real solutions)
Therefore, in the given situation we know that the equation X²+6x=5 has (3) two real solutions.
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A survey was given asking whether they watch movies at home from Netflix, Redbox, or a video store. Use the results to determine how many people use Redbox.
42 only use Netflix
44 only use Redbox
12 only use a video store
11 use only a video store and Redbox
42 use only Netflix and Redbox
33 use only a video store and Netflix
10 use all three
27 use none of these
How any people just use RedBox?
Answer:69
Step-by-step explanation: 32+420-90+09=69 pls mark it 5 stars
When expressions of the form (x −r)(x − s) are multiplied out, a quadratic polynomial is obtained. For instance, (x −2)(x −(−7))= (x −2)(x + 7) = x2 + 5x − 14.
a. What can be said about the coefficients of the polynomial obtained by multiplying out (x −r)(x − s) when both r and s are odd integers? when both r and s are even integers? when one of r and s is even and the other is odd?
b. It follows from part (a) that x2 − 1253x + 255 cannot be written as a product of two polynomials with integer coefficients. Explain why this is so.
a.(1) When both r and s are odd integers, the quadratic polynomial obtained by multiplying out (x - r)(x - s) will have a coefficient of 1 for x^2 term, and both the coefficient of x term and constant term will be odd integers.
(2) When both r and s are even integers, the polynomial obtained by multiplying out (x - r)(x - s) will also have a coefficient of 1 for x^2 term, but the coefficient of x term and constant term will be even integers.
(3) When one of r and s is even and the other is odd, the polynomial obtained by multiplying out (x - r)(x - s) will have a coefficient of 1 for x^2 term, the coefficient of x term will be an odd integer, while the constant term will be an even integer.
b. x^2 - 1253x + 255 cannot be written as a product of two polynomials with integer coefficients.
a. When both r and s are odd integers, the product (x − r)(x − s) will have a coefficient of 1 for x^2 term, and both the coefficient of x term and constant term will be odd integers. This is because the sum of two odd integers and the product of two odd integers is also an odd integer.
When both r and s are even integers, the product (x − r)(x − s) will also have a coefficient of 1 for x^2 term, but the coefficient of x term and constant term will be even integers. This is because the sum of two even integers and the product of two even integers is also an even integer.
When one of r and s is even and the other is odd, the product (x − r)(x − s) will have a coefficient of 1 for x^2 term, and the coefficient of x term will be an odd integer, while the constant term will be an even integer. This is because the sum of an odd and even integer is an odd integer, and the product of an odd and even integer is an even integer.
b. If x^2 - 1253x + 255 can be written as a product of two polynomials with integer coefficients, then we can write it as (x - r)(x - s) where r and s are integers. From part (a), we know that both r and s cannot be odd integers since the coefficient of x term would be odd, but 1253 is an odd integer. Similarly, both r and s cannot be even integers since the constant term would be even, but 255 is an odd integer. Therefore, one of r and s must be odd and the other must be even. However, the difference between an odd integer and an even integer is always odd, so the coefficient of x term in the product (x - r)(x - s) would be odd, which is not equal to the coefficient of x term in x^2 - 1253x + 255. Hence, x^2 - 1253x + 255 cannot be written as a product of two polynomials with integer coefficients.
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Of the clients at Dillon's salon, 4 clients have blond hair and 12 clients have hair in other
colors.
What is the probability that a randomly selected client at Dillon's salon has blond hair?
Write your answer as a fraction or whole number.
P(blond) =
In response to the stated question, we may state that As a result, the probability of a randomly picked client at Dillon's salon having blond hair is one-quarter.
What is probability?Probabilistic theory is a branch of mathematics that calculates the likelihood of an event or proposition occurring or being true. A risk is a number between 0 and 1, with 1 indicating certainty and a probability of around 0 indicating how probable an event appears to be to occur. Probability is a mathematical term for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. In relation to all other outcomes, the ratio of occurrences among equally likely alternatives that result in a certain event.
Dillon's salon has 4 clients with blond hair and 12 clients with different hair colours, for a total of 4+12=16 clients.
The chance of picking a blond-haired customer is equal to the number of blond-haired clients divided by the total number of clients:
P(blond) = number of blond clients / total number of clients = 4 / 16 = 1/4
As a result, the likelihood of a randomly picked client at Dillon's salon having blond hair is one-quarter.
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P(blond) = 4/16 = 1/4 .is the probability that a randomly selected client at Dillon's salon has blond hair.
What is probability ?Probability is a measure of the likelihood that an event or experiment will occur. It is expressed as a number between 0 and 1, with 0 meaning that the event is impossible to occur and 1 meaning that the event is certain to occur. Probability can be calculated using a variety of methods depending on the type of problem. For example, the probability of a coin being heads can be calculated by dividing the number of heads by the total number of coin flips.
Probability theory is an important part of statistics and is used to make predictions about the likelihood of certain events occurring. It is also used to assess risk and make decisions in a wide range of fields, from economics and finance to medicine and engineering.
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How this app works? Why I can’t find any answers? I need pay for points when I ask questions? I subscribe this app and when I’m lucky to the answers almost the answers are wrong
What are inequalities?
Answer:
In mathematics, an inequality is a statement that compares two values, indicating that they are not equal, and specifies the relationship between them. In other words, an inequality expresses a relative difference between two values or quantities, rather than an exact equality.
There are different types of inequalities, but the most common ones involve comparisons between numerical values or algebraic expressions using inequality symbols, such as:
Greater than: x > y (read as "x is greater than y")
Less than: x < y (read as "x is less than y")
Greater than or equal to: x ≥ y (read as "x is greater than or equal to y")
Less than or equal to: x ≤ y (read as "x is less than or equal to y")
Inequalities can also involve multiple variables and can be used to describe ranges of values or conditions that must be satisfied. For example, x + y > 5 is an inequality that describes a region of the xy-plane where the sum of x and y is greater than 5.
Inequalities are used extensively in many areas of mathematics, including algebra, calculus, and optimization, and also have applications in other fields such as economics, physics, and engineering.
Step-by-step explanation:
JJ fills in the grid of numbers below so that the sum of the first three numbers is 100, the sum of the middle three numbers is 200, and the sum of the last three numbers is 300. What is the filled in grid?
10 Fill in the three boxes 130
Answer:
Can you rephrase the question as it doesn't seem possible to solve. There may be a value missing.
Do X4 and 15+ X have the same value when X is 5
I will mark you brainiest!
What is the length of EF?
A) 2.4
B) 3.8
C) 0.5
D) 1.2
Answer:
the answer is 2.4 for ef
pls mark me brainliest
Question 6
One gallon of water weighs 8.34 lb. How much weight is added to a fire truck when its tank is filled
with 750 gal of water?
Question 7
1
Answer
6255 pounds
8.34×750=6255lbs
Chaz is a college student. He has a checking account balance of -$52.00. His roommate Will's
checking account balance is -$59.25. Chaz thinks that Will owes more to the bank than Chaz
does. Is Chaz correct? Explain your answer.
Answer: No, Chaz is not correct. Although their balances are both negative, we cannot compare them simply based on their numeric values. The magnitude of the balance does not indicate who owes more to the bank, as it depends on various factors such as account activity, fees, and interest rates. We would need to know more information about their accounts, such as the interest rates and any fees, in order to determine who owes more to the bank.
Excluding the bank fees Chaz would technically be correct.
No, Chaz is not correct.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
No, Chaz is not correct.
Although both Chaz and Will have negative checking account balances, we cannot determine who owes more to the bank based solely on the balance amount.
The balance amount only indicates how much money they owe to the bank, but it does not give any information about the amount they initially deposited or any other financial transactions they may have made.
To determine who owes more to the bank, we would need to know the initial deposit amount, the transaction history, and any fees or interest charges that have been applied to the accounts.
Without this additional information, we cannot accurately compare the two balances or determine who owes more to the bank.
Thus,
No, Chaz is not correct.
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Select the description of the graph created by the equation 3x2 – 6x + 4y – 9 = 0. Parabola with a vertex at (1, 3) opening left. Parabola with a vertex at (–1, –3) opening left. Parabola with a vertex at (1, 3) opening downward. Parabola with a vertex at (–1, –3) opening downward.
A parabola with a vertex at (1,3) and an opening downhill is depicted by the equation.
Describe a curve.A parabola is an equation of a curve with a spot on it that is equally spaced from a fixed point and a fixed line.
In mathematics, a parabola is a roughly U-shaped, mirror-symmetrical plane circle. The same curves can be defined by a number of apparently unrelated mathematical descriptions, which all correspond to it. A point and a line can be used to depict a parabola.
Equation given: 3x² - 6x + 4y - 9 = 0. When the given equation's graph is plotted, it is discovered that the parabola that is created is opened downward and has a vertex at the spot. ( 1,3). The graph and the following response are attached.
The equation that depicts a parabola with a vertex at (1,3) opening downward is option C, making it the right choice.
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Answer:
Parabola with a vertex at (1, 3) opening downward.
Step-by-step explanation:
please help fast!! brainliest!! Find the slope of a line perpendicular to the line whose equation is 4x − 6y = −24
Fully simplify your answer.
The slope of the sole sequence's perpendicular line is [tex]-\frac{3}{2}[/tex].
What is the perpendicular direction?As two lines meet at right angles, the word "perpendicular" refers to an angle. Every direction, including up and down, across, and side to side, can be faced by a pair of perpendicular lines.
Is a straight line considered to be perpendicular?A perpendicular is a straight line in mathematics that forms a correct angle (90 °) with another line. In other words, two lines are parallel to one another if they connect at a right angle.
[tex]y = mx + b[/tex], where [tex]m[/tex] is the slope:
[tex]4x - 6y = -24[/tex]
[tex]-6y = -4x - 24[/tex]
[tex]y = (4/6)x + 4[/tex]
[tex]y = (2/3)x + 4[/tex]
So the slope of the given line is [tex]2/3[/tex].
To find the slope of a line perpendicular to this line, we need to take the negative reciprocal of [tex]2/3[/tex]:
[tex]-1/(2/3) = -3/2[/tex]
Therefore, the slope of a line perpendicular to the given line is [tex]-\frac{3}{2}[/tex].
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Please help ASAP!!!! The average of two numbers is 13.One number is 10.What is the other number?
Answer:16
Step-by-step explanation:
average is similar to mean
you get the Total value and divide it with the number of values added
Find the length of AD in the figure.
A. 34 units
B. 122 units
C. 130 units
D. 26 units
The length of quadrilateral ABCD of AD, which is closest to option A, is [tex]4*sqrt(13)[/tex] (34 units).
Is a triangle 90 degrees or 180?A triangle will always have an angle total of 180 degrees. A quadrilateral can be divided in half from corner to corner to form a triangle because the angle total of a quadrilateral is equal to 360°. A triangle is effectively half of a quadrilateral, therefore it makes sense that its angle measurements are also half. 180° is the half of 360°.
The Pythagorean theorem can be used to calculate the duration of AD.
The distance formula can be used to get the length of AB first:
[tex]AB = sqrt((4-(-4))2 + (6-(-2))2 = sqrt(8-(-8-8) + 8-(8) = 8*sqrt (2)[/tex]
The distance formula can then be used to get the length of AC:
[tex]Sqrt((12-(-4)) = AC^2 + (6-(-2))^2)= sqrt(16^2 + 8^2) = 8*sqrt(5) (5)\\[/tex]
Now, we can calculate the length of AD using the Pythagorean theorem:
[tex]AD^2 = AB^2 + BD^2AD^2 = (8sqrt(2))^2 + (4sqrt(5))^2AD^2 = 128 + 80AD^2 = 208AD = sqrt(208)[/tex]
Simplifying the radical, we get:
AD = sqrt(1613) = 4sqrt(13)
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The length of quadrilateral ABCD of AD, which is closest to option A, is (34 units). Thus, option A is correct.
What is the sum of the angles in a triangle?The sum of the angles in a triangle is always 180 degrees. Because a quadrilateral's total angles are 360°, it can be divided in half from a corner to create a triangle.
The distance formula can be used to get the length of AB first: [tex]AB = sqrt((4 — (-4))2+ (6— (-2))2 = sqrt(8 — (-8— 8)+8— (8) = 8* sqrt(2)[/tex] The distance formula can then be used to get the length of AC:
[tex]Sqrt((12 — (-4)) = AC2 + (6 — (-2))2) = sqrt(162 + 82) = 8* sqrt(5)(5)[/tex]
Now, we can calculate the length of AD using the Pythagorean theorem:
[tex]AD2 = AB2 + BD2AD2 = (8sqrt(2))2 + (4sqrt(5))2AD2 = 128 + 80AD2 = 208AD = sqrt(208)[/tex]
Simplifying the radical, we get: [tex]AD = sqrt(1613) = 4sqrt(13)[/tex]
Therefore, It makes obvious that since a triangle is functionally half of a quadrilateral, its angle measurements are also half. Half of a 360° circle is 180°.
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Homer's car weighs 4,000 pounds. How many tons does
Homer's car weigh?
Answer:2
Step-by-step explanation:
Answer:
2 Tons
Step-by-step explanation:
Homer’s car weighs 2 tons because there are 2,000 pounds in a ton and 4,000 divided by 2,000 equals 2
Find the domains of the following functions:
f(x) = 2x + 7.
h(x) = (x-6)/(2x - 8)
The domain of the given function f(x) = 2x + 7 is -∞ < x < ∞.
What is a domain?The range of values that we are permitted to enter into our function is known as the domain of a function.
Consider the function y = f(x), which has the independent variable x and the dependent variable y.
A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.
So, the given function is:
f(x) = 2x + 7
To find the domain:
There are no undefined places or domain restrictions in the function. As a result, -∞ < x < ∞ is the domain.
Therefore, the domain of the given function f(x) = 2x + 7 is -∞ < x < ∞.
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Correct question:
Find the domains of the following function: f(x) = 2x + 7
The amount of paint needed to cover a wall is proportional to its area. The wall is rectangular and has an area of 6z^2 + 6z square meters. Factor this polynomial to find possible expressions for the length and width of the wall. (Assume the factors are polynomials.)
We can factor the polynomial 6z² + 6z as follows:
[tex]6z^2 + 6z = 6z(z + 1)[/tex]
We can use this factorization to express the area of the wall as the product of two factors:
[tex]6z^2 + 6z = 6z(z + 1) = length × width[/tex]
Therefore, the length of the wall is 6z, and the width of the wall is z + 1.
Daisy cream is sold in a bulk of 76 cups of cream. Kremlin cream is sold in a bulk of 4 1/2 gallons of cream. Mable cream is sold in a bulk of 40 pints. Which one has the most cream?
Answer:
Step-by-step explanation:
it is mable
Determine which points lie on the line L whose parametric or normal form is given. Circle all that afpjply: (c)L(x0,v) where x0 = 132 and v= −211 (5,1,0)(5,1,1)(1,3,2)
The points that lie on the line L with parametric form L(t) = (1, 3, 2) + t(-2, 1, -1) are (1, 3, 2), (-1, 4, 1), and (-3, 5, 0). So, the correct answer is C).
The parametric form of the line L can be written as:
L(t) = x0 + tv
where x0 = (1, 3, 2) and v = (-2, 1, -1)
To find which points lie on the line L, we can substitute different values of t into the parametric equation and see which points we get.
For t = 0, we have:
L(0) = x0 + 0v = (1, 3, 2) + 0(-2, 1, -1) = (1, 3, 2)
For t = 1, we have:
L(1) = x0 + 1v = (1, 3, 2) + (-2, 1, -1) = (-1, 4, 1)
For t = 2, we have:
L(2) = x0 + 2v = (1, 3, 2) + 2(-2, 1, -1) = (-3, 5, 0)
So the points that lie on the line L are (1, 3, 2), (-1, 4, 1), and (-3, 5, 0). So, the correct option is C).
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State if the triangles in each pair are similar
Answer:
They are similar
Step-by-step explanation:
It's because 27/18 = 12/8
27/18 = 1.5
12/8 = 1.5
given the following limit lim(x;y)!(0;0) infinty y infinity y , show that the function f (x; y) does not have a limit as (x; y) ! (0; 0).
The limit of f(x, y) as (x, y) approaches (0, 0) depends on the path taken, the limit does not exist, and we can conclude that the function f(x, y) do not have a limit as (x, y) → (0, 0).
To show that the function f(x, y) does not have a limit as (x, y) → (0, 0), we need to show that the limit does not exist, either because the limit is infinite or because the limit does not exist.
We are given that the limit of f(x, y) as (x, y) → (0, 0) when y → infinity is infinity. This means that as y approaches infinity, the function f(x, y) becomes arbitrarily large, regardless of the value of x. However, this does not imply that the limit of f(x, y) exists as (x, y) → (0, 0).
To see why, consider the sequence of points (x_n, y_n) = (1/n, n) as n approaches infinity. As y_n → infinity, we have
lim (x_n, y_n) → (0, 0) f(x_n, y_n) = infinity.
However, if we consider the sequence of points (x_n, y_n') = (1/n, n^2) instead, as n approaches infinity, we have
lim (x_n, y_n') → (0, 0) f(x_n, y_n') = 0.
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If 20 is 20% of 20% of an integer, what is that integer?
F. 20
G. 50
H. 200
J. 500
K. 1000
Answer:
J. 500
Step-by-step explanation:
20 percent is 0.2 when multiplying.
0.2(0.2(x)) = 20
0.04(x) = 20
x = 500
y varies inversely with x.
y = 15when x = 10
Find y when x = 5
Answer:
y=10
Step-by-step explanation:
Just needing help here
Based on the graph given, the function is not continuous at x = 1.
What is function?In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output. A function is typically represented using functional notation as f(x), which means that the output value of the function f corresponds to the input value x. Functions can take many forms and can be represented graphically or algebraically. They are used to describe many real-world phenomena, including physical systems, economic trends, and social behavior. Functions are important in mathematics because they provide a framework for understanding relationships between variables and for solving problems in various areas of mathematics, science, and engineering.
Here,
At x = 1, there is a "hole" or a point of discontinuity in the graph where the function is undefined. This is because the function has a removable discontinuity at x = 1, meaning that the limit of the function exists at x = 1 but the function is not defined at that point.
Therefore, the value of x at which the function is not continuous is: 1
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Simplify:
(cos^2(a)-cot^2(a))/sin^2(a)-tan^2(a)
Simplify the expression:
[tex]\dfrac{cot^2(a)(1+csc(a))(1-csc(a))}{(1+sec(a))(1-sec(a))}[/tex]