A. f(x) = 2|2| is differentiable overf
X
B. g(x) = 2 + || is differentiable over
-f
Answers
Recall the definition of absolute value:
• If x ≥ 0, then |x| = x
• If x < 0, then |x| = -x
(a) Splitting up f(x) = x |x| into similar cases, you have
• f(x) = x ² if x ≥ 0
• f(x) = -x ² if x < 0
Differentiating f, you get
• f '(x) = 2x if x > 0 (note the strict inequality now)
• f '(x) = -2x if x < 0
To get the derivative at x = 0, notice that f '(x) approaches 0 from either side, so f '(x) = 0 if x = 0.
The derivative exists on its entire domain, so f(x) is differentiable everywhere, i.e. over the interval (-∞, ∞).
(b) Similarly splitting up g(x) = x + |x| gives
• g(x) = 2x if x ≥ 0
• g(x) = 0 if x < 0
Differentiating gives
• g'(x) = 2 if x > 0
• g'(x) = 0 if x < 0
but this time the limits of g'(x) as x approaches 0 from either side do not match (the limit from the left is 0 while the limit from the right is 2), so g(x) is differentiable everywhere except x = 0, i.e. over the interval (-∞, 0) ∪ (0, ∞).
Related Questions
A computer technician charges $60 for coming to your house plus $76 per hour for labor. If the total bill for repairs is $269, how long did the work take?
Answers
Answer:
[tex]2\frac{3}{4}[/tex] or 2.75, depending on what you need.
Step-by-step explanation:
Subtract $269 by the service fee ($60). This will be $209.Divide $209 by $76 to calculate hours. This will be 2.75.(optional) We know that 0.75 is [tex]\frac{3}{4}[/tex], so let's take 2.75 and convert it into [tex]2\frac{3}{4}[/tex]. This is your answer.Find the missing value.
Hint: Use the number line to find the missing value.
Answers
hope this helps!
The answer is -12! Good luck!
Extend the pattern below by four terms write an observation about the pattern pattern 76, 70, 64,58,52
Answers
Answer:
46, 30, 24, 18, 12
Step-by-step explanation:
Which of the following lines goes through the point (0,4) and is parallel to y = 5 x - 3?
M
O =
y = 5 x + 4
W
y= 5 x-7
y = -5 X-3
Answers
y=5x-7 is also parallel to y=5x-3 although it doesn’t go through point (0,4)
y=-5x-3 is obviously not parallel to y=5x-3 because it intersects to it
Is a=2.1, b=7.2, c=7.5 a right triangle?
Answers
Answer:
Yes
Step-by-step explanation: Use the pythagorean theorem to see if true, a^2+b^2=c^2
Answer:
Yes it is
Step-by-step explanation:
2.1
3.
On a coordinate plane, a line segment has P(6,2) and Q(3,8).
Point M lies on PQ and divides the segment so that the ratio
of PM:MQ is 3:2. What are the coordinates of point M?
A. (4.5, 5.0)
B. (5.6, 4.2)
C. (4.8, 4.4)
D. (4.2, 5.6)
Answers
Answer:
[tex]M(x,y) = (4.8,4.4)[/tex]
Step-by-step explanation:
Given
[tex]P(x_1,y_1) = (6,2)[/tex]
[tex]Q(x_2,y_2) = (3,8)[/tex]
[tex]m:n = PM:MQ = 3 : 2[/tex]
Required
Determine the coordinates of M
To solve this, we make use of the following partition formula:
[tex]M(x,y) = (\frac{nx_2+mx_1}{n+m},\frac{ny_2+my_1}{n+m})[/tex]
Substitute values for m, n, x's and y's
[tex]M(x,y) = (\frac{2*3+3*6}{2+3},\frac{2*8+3*2}{2+3})[/tex]
[tex]M(x,y) = (\frac{24}{5},\frac{22}{5})[/tex]
[tex]M(x,y) = (4.8,4.4)[/tex]
Option D is correct
Given the following sets:
A = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
B = {3, 6, 9, 12, 15, 18}
C = {4, 8, 12, 16, 20}
Find:
n (A)
Answers
Answer:
n (A) = { 2,4,6,8,10,12,14,16,18,20}
n(A) = 10
I hope it helps
A telephone pole has a wire attached to its top that is anchored to the ground. The distance from the bottom of the pole to the anchor point is 51 feet less than the height of the pole. If the wire is to be 24 feet longer than the height of the pole, what is the height of the pole?
Answers
Answer:
Height is 135 ft
Step-by-step explanation:
Notice that wire, pole, and ground form a right angle triangle, for which we name h = height of the pole one of the legs (the horizontal leg) is h - 51. The wire (which is the hypotenuse of the right angle triangle is: h + 24.
Then we can use the Pythagorean theorem to solve for the height (h):
h^2 + (h - 51)^2 = (h + 24)^2
h^2 + h^2 -102 h + 2601 = h^2 + 48 h + 576
grouping all terms on the left of the equal sign, we get:
h^2 -150 h + 2025 = 0
This gives two possible answers:
h = 135
and
h = 15
We opt for h = 135, because the other solution will render a negative leg for the triangle.
A copy machine makes 28 copies per min. How long does it take to make 119 copies?
Answers
Answer:
4 minutes and 15 seconds
Step-by-step explanation:
119/28 = 4.25 (minutes)
.25 of a minute is 15 seconds, so the answer is 4 minutes and 15 seconds
There are 750 students at school. The ratio of the number of students who do not wear glasses to the number of students who wear glasses is 500:250. Which of the following statements are correct? Select ALL that apply.
Answers
Answer:
what are the options
Step-by-step explanation:
Check all the statements that are true:
a. A predicate is a proposition-valued function.
b. It is possible to define disjunction using only negations and conjunction.
c. A conditional is false when both premise and conclusion are false.
d. Domain-restricted universal quantification is logically equivalent to the unrestricted universal quantification of a conditional.
e. The negation of a conjunction is the disjunction of the negations.
f. Inverse and converse are logically equivalent.
g. (p→q)∧(p→¬q) is a contradiction.
h. (p→q)∨(p→¬q) is a tautology.
i. Domain-restricted existential quantification is logically equivalent to the unrestricted existential quantification of a conditional.
j. The contrapositive is the inverse of the converse.
Answers
Answer:
a. True
b. False
c. True
d. True
e. False
f. True
g. False
h. True
i. True
j. True
Step-by-step explanation:
The statement a and i are true. The predicates can be defined without an input variable. These numerical variables can be defined without an input variable. The statement b is false since the p to q is not in conjunction rather its contradiction.
Answer:
true
false
true
true
false
true
false
true
true
true
Fourth eight time four
Answers
Answer:
2
Step-by-step explanation:
We have a multiplication problem within a whole number and a fraction.
When multiplying fractions with whole numbers, you always multiply the whole number with the numerator of the fraction.
[tex]\frac{numerator}{denominator}[/tex]
[tex]\frac{4}{8} *4[/tex]
[tex]\frac{4*4}{8}[/tex]
[tex]\frac{16}{8}[/tex]
Divide 16 by 8 :
[tex]2[/tex]
Find the diffrence between 7/8 and 1/2 and find the sum of 1/5 and 2/3
Answers
Answer:
3/8 and 13/15
Step-by-step explanation:
find the common denominator
A person places $85800 in an investment account earning an annual rate of 8.5%,
compounded continuously. Using the formula V = Pert, where V is the value of the
account int years, P is the principal initially invested, e is the base of a natural
logarithm, and r is the rate of interest, determine the amount of money, to the nearest
cent, in the account after 9 years.
Answers
Answer:
$184383.7
Step-by-step explanation:
We are given that
Principal, P=$85800
Rate of interest, r=8.5%=0.085
Time, t=9 years
We have to find the amount of money after 9 years
[tex]V=Pe^{rt}[/tex]
Using the formula
[tex]V=85800e^{0.085\times 9}[/tex]
[tex]V=184383.7[/tex]
Hence, the amount of money after 9 years=$184383.7
12. The win-loss record for a football team is 15 wins and 9 losses. What percent of their games
did they win?
Answers
Answer:
62.5%
Step-by-step explanation:
if they won 15 and lost 9 games then they played a total of 24 games (15+9). Then you just divid the number of wins (15) by the total number of games they played (24). SO, 15/24=0.652 or 62.5%
Q1: In the isosceles triangle below the legs are twice the
length of the base. The perimeter is 100 cm. What are the
dimensions of the isosceles triangle?
Answers
Answer:
The base of the triangle has a size of 20 cm, while each side has a size of 40 cm.
Step-by-step explanation:
An isosceles triangle is one that has two sides with an identical value, and one side with a different value from the previous ones. Thus, in the case the base will have a different value from the sides. In this regard, the perimeter (the sum of the sides) of the triangle is 100 cm, and the longest sides are twice the size of the base. Therefore, to determine the value of each side of the triangle, the following calculation must be performed:
X + 2X + 2X = 100
5X = 100
X = 100/5
X = 20
Thus, the base of the triangle has a size of 20 cm, while each side has a size of 40 cm.
This table shows how long, in minutes, it takes Jeremiah to run his miles.
How long does it take him to run 5 miles? *
Answers
Answer:
45
Step-by-step explanation:
follow the table of 9.
9x2=18
9x3=27
9x4=36
9x5=45
Caleb is making lemonade and cookies for the school bake sale. He has 10 cups of
sugar. He needs two cups of sugar for lemonade. Each batch of cookies uses 11/2 cups
of sugar. What is the maximum number of cookie batches he can make?
Answers
Answer:
He can make only one batch of cookies.
Step-by-step explanation:
Just by mental math you can say he can make maximum one batch of cookies.
Total sugar = 10 cups
sugar used for lemonade = 2 cups
leftover sugar = 8 cups
For 1 batch of cookie sugar needed = 11/2
which means 5 and 1/2 cups
And he's just left with 8 cups of sugar after lemonade
8 - 5 1/2 = 2 1/2 which is not enough for 2nd batch
That means the maximum number of cookies batches is 1.
Another way to solve it by inequality:
2+Il/2 X < 10
11/2 X < 8
11X < 16
X < 1 6/11
So he can make only one batch of cookies.
(3x ^ 2 - 4 + x ^ 3) / (x - 1)
Synthetic Division
Answers
Answer:
i love algebra anyways
the ans is in the picture with the steps
(hope it helps can p lz have brainlist it will make my day
Step-by-step explanation:
Hurry pls need answers
10pts
Answers
Answer:
Why is the pic black
Step-by-step explanation:
In 1990, the cost of tuition at a large Midwestern university was $99 per credit hour. In 2003, tuition had risen to $268 per credit hour
Answers
Answer:
63%
Step-by-step explanation:
From the question, we aim to find the percent increase in the tuition
Given data
initial cost= $99 per credit hour
Final cost= $268 per credit hour
% increase= (Final - initial )/initial *100
substitute
% increase= (268- 99 )/268 *100
% increase= 169 /268 *100
% increase= 0.630*100
% increase= 63%
Hence the increase in the tuition from 1990 to 2003 is 63%
taria has 14 pencils, Ted has 9 pencils, Tom has 12
encils, Lucinda has 13 pencils, and Jumana has 12
encils How can they redistribute the pencils so that
they all have the same amount How many pencils
hould each person have
Answers
Answer:
that would all have 7 pencils each
Answer:
Maria should give away 2 pencils. Ted should get 3 pencils. Lucinda should give away 1 pencil. Everyone should have 12 pencils.
Find c.
Round to the nearest tenth:
Answers
Answer:
Step-by-step explanation:
2/Sin(105) = c / sin(15)
2 * sin(15) = c * sin(105) Divide by Sin(105)
2 * sin(15)/Sin(105) = c
2 * 0.2679 = c
c = 0.539
c = 0.5
Which of the following expressions is equivalent to 1 over 4 open parentheses 8 x plus 12 close parentheses ?
A: 2x+12
B: 5x
C: 2x+3
D: 14x
Answers
Because... 1/4(8x+12)
multiply 1/4 into 8x and into 12 (use pemdas if confused)
1/4 by 8X is 2x... same as 8/4
1/4 by 12 is 3... same as 12/4
Find the surface area of this rectangular prism: Don't forget to show the unit of measure.
Answers
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete as the attachment of the prism is not given.
From the attachment:
[tex]L =10cm[/tex] -- Length
[tex]W = 4cm[/tex] -- Width
[tex]H=5cm[/tex] -- Height
Required
Determine the volume
So, the volume is:
[tex]Volume = Length * Width (* Height[/tex]
[tex]Volume = 10cm * 4cm * 5cm[/tex]
[tex]Volume = 200cm^3[/tex]
what is 6 more than -3 in integers
Answers
Answer:
3
Step-by-step explanation:
-3 + 6 would be 3.
hope it helps!
- More than means ‘ > ’
- Less than means ‘ < ’
- More than or equal to means ‘ ≥ ’
- Less than or equal to means ‘ ≤ ’
Jamey has 4 quarters, some dimes, and some pennies. If the ratio of quarters to dimes is 8 : 6 and the ratio of pennies to dimes is 7 : 3, then how many pennies does Jamey have?
Answers
Answer:
7
Step-by-step explanation:
the ratio of [pennies to dimes is 7:3.... 7 represents pennies and 3 dimes
By the given ratio, Number of pennies does Jamey have are 7.
What is a ratio?"A ratio compares values. A ratio says how much of one thing there is compared to another thing."
According to the question
Jamey has 4 quarters, some dimes, and some pennies.
Ratio of quarters to dimes is 8:6
So, [tex]\frac{4}{d}=\frac{8}{6}[/tex]
⇒ [tex]8d = 6(4)[/tex]
⇒ [tex]d=\frac{6}{2}[/tex]
⇒ [tex]d=3[/tex]
Ratio of pennies to dimes is 7 : 3
So, [tex]\frac{p}{d}=\frac{7}{3}[/tex]
By substituting d = 3
⇒ [tex]\frac{p}{3}=\frac{7}{3}[/tex]
⇒ [tex]p = \frac{7}{3}(3)[/tex]
⇒ [tex]p =7[/tex]
Hence, number of pennies does Jamey have are 7.
Learn more about ratio here
https://brainly.com/question/10167786
#SPJ2
The price of oil decreased from $52 per barrel to $48 per barrel. What is the percentage decrease in the price of oil? Round your answer to the nearest tenth of a percent.
Answers
Answer:
7.7%
Step-by-step explanation:
Given that,
The price of oil decreased from $52 per barrel to $48 per barrel.
We need to find the percentage decrease in the price of oil. It can be calculated as follows :
[tex]\%=\dfrac{52-48}{52}\times 100\\\\=7.69\%[/tex]
or
= 7.7%
So, the percentage decrease in the price of oil is 7.7%.
Answer:7.7%
Step-by-step explanation:
Write 10 3 without an exponent what number Is this ? 5.102+ 3
Answers
The value of 10^3 in standard form is 1000
Exponents and valuesGive the exponential form 10^3
This means the product of 10 in 3 places. Mathematically;
10^3 = 10 * 10 10 * 10
10^3 = 100 * 10
10^3 = 1000
Hence the value of 10^3 in standard form is 1000
Learn more on standard form here: https://brainly.com/question/19169731
Homework 9.4 Equations and Word Problems
The flag of a country contains in the senseless triangle if the measure of the third angle of the triangle is 30° more than twice the measure of either of the other two angles find the measure of each angle of the triangle
Answers
Answer:
idc
Step-by-step explanation: