Evaluate the following
Lim (xcotx)
x->00

Answers

Answer 1

Answer:

1

Step-by-step explanation:

Evaluate the following

Lim (xcotx)

x->0

Note that cotx = cosx/sinx

The expression becomes

Lim (xcotx) = Lim (xcosx/sinx)

x->0               x->0

= 0cos0/sin0

= 0/0 )(ind)

Apply l'hospital rule

= Lim d/dx(xcosx/sinx)

x->0          

= lim (-xsinx + cosx)/cosx

    x->0

= -0sin0+cos0/cos0

= 0+1/1

= 1/1

= 1

Hence the limit of xcotx as x tends to zero is 1      


Related Questions

-595-65

Btw they are both negative numbers

Answers

Answer:

-660

Step-by-step explanation:

-595-65=-660

Here you goooo!!!!!!!!!!

Show how you found the slope and y-intercept

Answers

Answer:

Slope: [tex]\frac{5}{2}[/tex]

y-intercept: 0

Step-by-step explanation:

First, find the slope. Use two points given to you. In this case, I will use the following:

(x₁ , y₁) = (2 , 5)

(x₂ , y₂) = (4 , 10)

Use the following equation:

slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in the corresponding numbers to the corresponding variables:

slope (m) = [tex]\frac{10 - 5}{4 - 2}[/tex] = [tex]\frac{5}{2}[/tex]

Note the slope intercept form:

y = mx + b

y = (x , y)

m = slope

x = (x , y)

b = y-intercept

Plug in the slope into m for the equation:

[tex]y = \frac{5}{2} x + b[/tex]

Choose a point to use to find b. In this case, I will use (2 , 5). Plug in 2 for x, and 5 for y:

[tex]5 = \frac{5}{2}(2) + b[/tex]

Simplify. Isolate the variable, b. Note the equal sign, what you do to one side, you do to the other:

[tex]5 = \frac{5}{2}(2) + b\\5 = 5 + b\\5 (-5) = 5 (-5) + b\\b = 5 - 5\\b = 0[/tex]

Y-intercept: 0

A person invested $370 in an account growing at a rate allowing the money to double every 11 years. How long, to the nearest tenth of a year would it take for the value of the account to reach $720

Answers

Answer:

10.6

Step-by-step explanation:

y=a(2)^t/d

Plug in

720=370(2)^t/11

Divide both sides by 370

1.945945946 = (2)^t/11

Log both

Log(1.945945946) / Log(2)

0.9604716359 = t/11

0.9604716359 x 11 = t

10.56518799 to the nearest tenth is 10.6 = t

It would take 10.6 years for the value of the account to reach $720.

What is an exponential function?

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

A person put $370 into an account that grew at a rate that allowed the money to double every 11 years.

As per the question, we can write an exponential function as:

[tex]y=a(2)^{t/d}[/tex]

Substitute the values of y = 720, a = 370 and d = 11 in the above equation:

[tex]720=370(2)^{t/11}[/tex]

Divide both sides by 370

[tex]1.945945946 = (2)^{t/11}[/tex]

Take logarithms on both sides of the equation,

log(1.945945946) / log(2)

0.9604716359 = t/11

0.9604716359 x 11 = t

t = 10.56518799

Rounded to the nearest tenth

t = 10.6

Thus, the required time would be 10.6 years.

Learn more about exponential function here:

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Joe has $50.00. He wants to buy equal numbers of soft drinks and sandwiches. A soft drink costs $0.79. A sandwich costs $2.49. How many of each can joe buy with his $50.00? A.15 B.20 C.41 D.63 please help if you can!

Answers

Answer:

First you have to add the price of one soft drink and one sandwich which would be $3.28. Then divide 50 with 3.28 and you get 15.2439 approximately 15.

So your asnwer should be A. 15

Step-by-step explanation:

Can someone help me

Answers

Answer:

The first one is a right angle (90-degree angle) The second one is an acute and obtuse angle. And the slope is y=2x-3

Step-by-step explanation:

Hope this Helped

First one is a right angle because it is 90 degrees. Second is a acute angle because it is LESS than 90 degrees. Then third is a obtuse angle because it is MORE than 90 degrees

Hazel works at The Last Page Booksellers. Her total earnings were $24,000 last year. Hazel
paid $157 in payroll taxes for every $1,000 she earned.
What was Hazel's net income for last year?

Answers

Answer:

Step-by-step explanation:

157x24 = ...

Michael had 3 times as many mangoes as Junior. After eating 8 mangoes. Michael had
twice as many mangoes as Junior. What is the total number of mangoes both boys had at
the beginning?​

Answers

Answer:

Michael: 24

Junior: 8

Step-by-step explanation:

8 is a multiple of 24, meaning if you ate 1/3 of 24 you get 16, which is doubled 8.

Evaluate 7^2 PLEASE HELP ME

Answers

Evaluate 7^2 = 49
7•7=49

What is the area of the triangle? 4 6 units2​

Answers

4 x 6 x 2 = 24 x 2 = 48 ..

Please Help! One natural number is 4 more than the other one. The product of the two numbers is three times the square of the smaller number. Find the numbers.​

Answers

Let n and n+4 be the numbers. Then:

n² + 3(n+4)=66

n²+3n-54=0

(n+9)(n-6)=0

n=6 or -9

n+4=10

Assuming positive integers only, the numbers are 6 and 10…..

Step-by-step explanation:

100% right

Answer:

2 and 6

Step-by-step explanation:

Find the slope of the line that passes through Point A (-1, -6) and Point B (-7, -3), using the formula m= y2-y1/x2-x1.​

Answers

Answer:

Step-by-step explanation:

Given A (-1, -6) and  B (-7, -3)

Slope (m)

= y2-y1/x2-x1

= - 3 + 6 / - 7 + 1

= 3/-6

=-1/2

hope it helps :)

Answer: 3 / -6

Step-by-step explanation:

-3 - (-6) / -7 - - 1 = 3 / -6

The subtraction turns into addition because to “-“ equals “+” and if graphed the points will go up three units and six units to the left

Plss this is timed will mark brain least if shown work!

Answers

Answer:

I just answered this

do 62.31/3 which is 20.77 so 1 shirt cost 20.77

now do 20.77+3.66 which is 24.43

so the answer is C. $24.43

What is the least common denominator of 3/5 and 9/10?​

Answers

Answer:

9/10

Step-by-step explanation:

3/5 = 6/10 = 9/10 = 9/10

I'm not 100% sure of this answer someone please correct me if I'm incorrect.

30 POINTS PLS HELP
The slope of the linear function y= 5/4x +1/2 is changed to 5/8 where y= 5/8x + 1/2. Identify the transformation required to produce the new slope, state the equation of the transformed function, ande explainw hat the graph of the tranfsformed line look like.
Here is the picture of the question

Answers

Answer:

We proceed to use the following operations: (i) Vertical translation downwards ([tex]k = -\frac{1}{2}[/tex]), (ii) Vertical compression ([tex]c = \frac{1}{2}[/tex]), (iii) Vertical translation upwards ([tex]k = \frac{1}{2}[/tex]). The graph is presented below.

Step-by-step explanation:

To transform [tex]y = \frac{5}{4}\cdot x + \frac{1}{2}[/tex] into [tex]y = \frac{5}{8}\cdot x + \frac{1}{2}[/tex], we apply the following steps:

(i) Vertical translation downwards ([tex]k = -\frac{1}{2}[/tex])

[tex]g(x) = f(x) +k[/tex] (1)

(ii) Vertical compression ([tex]c = \frac{1}{2}[/tex])

[tex]g(x) = c\cdot f(x)[/tex] (2)

(iii) Vertical translation upwards ([tex]k = \frac{1}{2}[/tex])

[tex]g(x) = f(x) + k[/tex]

Now, we proceed to transform the primitive expression:

Step 1

[tex]f'(x) = \frac{5}{4}\cdot x[/tex]

Step 2

[tex]f''(x) = \frac{5}{8}\cdot x[/tex]

Step 3

[tex]g(x) = \frac{5}{8}\cdot x + \frac{1}{2}[/tex]

The graph of both function are now presented below. The parent function is the red line and the new function is represented by the blue line.

They boost the economy

Answers

Answer:

I think the question is incorrect

Step-by-step explanation:

they boost the economy why is this in mathematics

‍♀️‍♀️

NEEd help quickly please!!! The basketball game had 500 people in attendance. If the ratio of Pioneer fans to Lion fans is 15:5, how many MORE Pioneer fans were there? Pls use tape diagram.

Answers

Answer:

Step-by-step explanation:

15(500/20)-5(500/20)

375-125

250

There were 250 more Pioneer fans than Lion fans.

PLS HELP I DONT KNOW THIS ONE ITS URGENT

Answers

Answer:

A. [tex] \frac{UV}{VW} = \frac{ZY}{YX} [/tex]

Step-by-step explanation:

WX, VY, and UZ are parrelel to each other, therefore, base on triangle proportional theorem, the two transversal lines are divided proportionally by the 3 parallel lines.

Thus, we would have the following equation which is true:

[tex] \frac{UV}{VW} = \frac{ZY}{YX} [/tex]

Which expression is equivalent to x + 0.2x

1.2x
0.2x squared
0.2x
1.02x​

Answers

The answer to this expression would be 1.2x

What is the measure of angle A?
Enter your answer as a decimal in the box. Round your final answer to the nearest hundredth.

Answers

Answer: 45 degrees

Step-by-step explanation:

Answer is 45 degrees

Rewrite y=a(1/3)^3t in the form y = a(1+r)^t or y = a(1 –r)^t

Answers

Answer:

sorry

Step-by-step explanation:

sorry I cannot help u because I have not seen this type of question before and I have not learn I am in 7 classes

What is 16% as a decimal?

Answers

Answer:

0.16 in decimal

Step-by-step explanation:

Answer:

0.16

Convert to a fraction, then convert to a decimal by dividing the numerator by the denominator.

16/100

Then when you divide it, it becomes 0.16.

Paz has $18 in her wallet. This is 3 times the money in her pocket. Write and solve an equation to find how much money Paz has in her pocket.

Answers

3x=18

x= 6

6 dollars in pocket

Answer:

32+s=55

Step-by-step explanation:

Sarah is saving money to buy a jacket that costs $47. She has already saved $25. Write an equation to find out how much more money Sarah needs to save, using x, to represent how much more she needs to save.

The population of cats that are rescued every year is currently 50,000 and declines at a rate of 1.2% every year. This models

Answers

Answer:

Exponential decay

The perimeter of a triangle is 51 centimeters. The lengths of its sides are represented by x, x + 2 and x + 4. Find the lengths of all three sides.

Answers

Answer:

sides are 15 cm, 17 cm, and 19 cm

Step-by-step explanation:

x + (x+2) + (x+4) = 51

3x+6 = 51

3x = 45

x = 15

Find the ratio of the following in the simplest form. 50 minutes to 1 hour

Answers

Answer:

5:6

Step-by-step explanation:

1 hour = 60 minutes

Ratio of 50 minutes to 1 hour;

50/60

5:6

Answer:

5:6

Step-by-step explanation:

1 hour= 60 min

50: 60

5:6

A polynomial function has zeros at 5/2 (multiplicity 2), 3 (multiplicity 1), and 0 (multiplicity 4). Write a function in standard form that could represent this function

Answers

Answer:

-75 x^4 + 85 x^5 - 32 x^6 + 4 x^7

Step-by-step explanation:

[tex](x-5/2)^{2}(x-3)(x-0)^4 =0\\(2x-5)^{2}(x-3)(x)^4 =0[/tex]

Expand and get

-75 x^4 + 85 x^5 - 32 x^6 + 4 x^7

The standard form will be  [tex]X^4(x^4-7x^3+12x^2-\dfrac{35x}{2} +\dfrac{25x^2}{4} +\dfrac{25}{4} =0[/tex]

What will be the standard form of the given expression?

The given expression is

[tex](x-\dfrac{5}{2})^2(x-1)^2(x-0)^4=0[/tex]

[tex](x^2-5x+\frac{25}{4} )(x^2-2x+1)(x^4)=0[/tex]

[tex](x^4-2x^3+x^2-5x^3+10x^2-5x+\dfrac{25x^2}{4} -\dfrac{50}{4} x+\dfrac{25}{4} ) x^4=0[/tex]

[tex]X^4(x^4-7x^3+12x^2-\dfrac{35x}{2} +\dfrac{25x^2}{4} +\dfrac{25}{4} =0[/tex]

Thus the standard form will be  

[tex]X^4(x^4-7x^3+12x^2-\dfrac{35x}{2} +\dfrac{25x^2}{4} +\dfrac{25}{4} =0[/tex]

To know more about Polynomials follow

https://brainly.com/question/15702527

if kya wins the election she will not be continuing to get in touch with her family/friends and now she has to make a decision to help people in need around the world she is 48 hours to decide if she will go or not she need to week to pack and they leave the day after because she says that yes how long would you have with her family/Friends​

Answers

Answer:

47 hours?

Step-by-step explanation:

She would have 47 hours lol

If she says yes then she would have enough time to spend with family and then 1 hour to go?

Can someone please help!!!

Answers

the answer is option 3

Answer: {t| t ≥ 2}

Step-by-step explanation:

3t - 6 ≥ t - 2

-t         -t

---------------------

2t - 6 ≥ -2

   +6    +6

---------------------

2t ≥ 4

t ≥ 2

Sydney's car used 1/ 3/5
gallons to travel 6666 miles. How many miles can the car go on one gallon of gas?

Answers

Answer:

Sydney car can go 44.4 miles on gallon

Please Help. Will give Brainliest.

Answers

Answer:

translation.........

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