lim x→π/2 1-sinx/cot^2x
any genious help please ​

Answers

Answer 1

Rewrite the limand as

(1 - sin(x)) / cot²(x) = (1 - sin(x)) / (cos²(x) / sin²(x))

… = ((1 - sin(x)) sin²(x)) / cos²(x)

Recall the Pythagorean identity,

sin²(x) + cos²(x) = 1

Then

(1 - sin(x)) / cot²(x) = ((1 - sin(x)) sin²(x)) / (1 - sin²(x))

Factorize the denominator; it's a difference of squares, so

1 - sin²(x) = (1 - sin(x)) (1 + sin(x))

Cancel the common factor of 1 - sin(x) in the numerator and denominator:

(1 - sin(x)) / cot²(x) = sin²(x) / (1 + sin(x))

Now the limand is continuous at x = π/2, so

[tex]\displaystyle\lim_{x\to\frac\pi2}\frac{1-\sin(x)}{\cot^2(x)}=\lim_{x\to\frac\pi2}\frac{\sin^2(x)}{1+\sin(x)}=\frac{\sin^2\left(\frac\pi2\right)}{1+\sin\left(\frac\pi2\right)}=\boxed{\frac12}[/tex]


Related Questions

Brandon has a points card for a movie theater. He receives 70 rewards points just for signing up. He earns 12.5 points for each visit to the movie theater. He needs 145 points for a free movie ticket. How many visits must Brandon make to earn a free movie ticket?

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Answer: x=6

Step-by-step explanation:

Answer:

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Step-by-step explanation:

Jennifer sets her binoculars to enlarge objects 10 times their actual size. If the length of an ant is 0.52 inches, what is its length as seen through her binoculars?

Answers

Answer:

The length as seen through her binoculars is of 5.2 inches.

Step-by-step explanation:

The length of an ant is 0.52 inches, what is its length as seen through her binoculars?

The binocular is set to enlarge the object 10 times their actual size.

We have that the actual length is 0.52 inches.

0.52*10 = 5.2 inches

The length as seen through her binoculars is of 5.2 inches.

Round 1231.50432 to the nearest tenth

Answers

Answer:

1231.5

Step-by-step explanation:

I hope this help.

Bianca makes an error when she tries to write an expression equivalent to
12 + 15(3 - y) - 10y. What is the error? Fix Bianca's error.
I NEED HELP ASAPPPPPP!!!

Answers

Answer:

57 - 25y

Step-by-step explanation:

when 15 was distributed it should be '45 - 15y' instead of '45 + 15y'

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The correct expression is

12 + 15(3 - y) - 10y

12 + 15 x 3 - 15y - 10y

12 + 45 - 15y - 10y

57 - 20y

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Step 1:

12 + 15(3 - y) - 10y

Step 2:

12 + 15 x 3 - 15y - 10y

Step 3:

12 + 45 - 15y - 10y

Step 4:

57 - 20y

Now,

We see that,

There was an error in step 2 where instead of -15y, +15y was written.

Thus,

The correct expression is

12 + 15(3 - y) - 10y

12 + 15 x 3 - 15y - 10y

12 + 45 - 15y - 10y

57 - 20y

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ5

2/5 > 1/2 or 2/5 <1/2

Answers

Answer:

It's 2/5 <1/2.

can someone help me with this

Answers

90000
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What is the answer
a3-c + b, when a=3,b=6, c=8​

Answers

Answer:

The answer is 25

Step-by-step explanation:

Y - 5= - (5 - y)
Does it have a solution?

Answers

Answer:

infanite

Step-by-step explanation:

how do u solve 5/2x-7=3/4x+14​

Answers

Answer:

x=12

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Simplify by combining like terms: 9xy-3y-y-2xy+3​

Answers

Answer:

7xy -4y + 3

Step-by-step explanation:

combine 9xy and -2xy (7xy - 3y -y +3)

combine -3y and -y (7xy - 4y + 3)

all done yay

Who can answer this

Answers

Answer:

Check pdf

Step-by-step explanation:

There are 20 pieces of fruit in a bowl and 8 of them are bananas. What percentage of the pieces of fruit in the bowl are bananas?




**choose your answer from the choices on Slide 5, but you must show how you got your answer on the chart, blank drawing space below, or explain in words**

Answers

The answer is that I got was the answer .4 because the fraction is 8/20 and that as a percentage is .4

David has 54 marbles, 24 of which are black, 18 are red, and 12 are blue. What fraction represents the ratio of black marbles to blue marbles?

Answers

24/12 or 1/2 (if you want it simplified)

This is because the number of black marbles are 24 and blue marbles are 12, you can just put into a fraction like that :)

solve for x. x+53=99 A.36 B.46 C.47 D.152​

Answers

Answer:

Hii, the answer B. 46

Step-by-step explanation:

x+ 53 = 99

So to find what x equals we just do simple subtraction

99 - 53 = 46

so x = 46

Hope this helps!

What is bigger 4.62 or 4.24

Answers

Answer: 4.62 is bigger than 4.24

Step-by-step explanation:

Compare the graphs of the functions listed below.

Function 1: y = 0.25x2

Function 2: y = 4x2

Function 3: y = -½x2

Function 4: y = -16x2

The graph of is the widest.

Answers

Answer:

The graph of FUNCTION 1 is the widest.

Step-by-step explanation:

So sorry lolll. But this is definitely right

What is the sum of the largest and smallest recorded capacity?

Answers

3.5
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If the number 45 is multiplied by 100, In what place value will the 4 be?
thousands
tens
ones
hundreds

Answers

Answer:

thousands

Step-by-step explanation:

the number would be 4,500

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Answers

Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

combine like terms

(10f -5f)

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Answers

Answer:

Step-by-step explanation:

12/5

as a mixed fraction 2 2/5

or as decimal 2.4

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Highly likely
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Answers

Answer:

well, highly likely. it will always fall on a monday,

Step-by-step explanation:

if you look at all of the years it has fallen on since 2010 you will see it has  always fallen on monday.

simplify the expression -2d + -2d - 9 + -9

Answers

Answer:

-4d-18

Step-by-step explanation:

Combine like terms:

-2d and -2d can combine since they have the same variable of d creating the term of -4d and -9 and -9 can combine to create -18. Put those together and you get the answer above.

Answer:

-4d-18

Step-by-step explanation:

Negative nine minus negative ten?

Answers

Answer:

-9 - 10 = -19

Step-by-step explanation:

If both numbers are a negative, then add them together but keep the negative or minus sign

Hope this Helps!!!

Which improper fraction is equivalent to 15 3/7

Answers

Answer:

108/7

Step-by-step explanation:

15*7 is 105+3 is 108/7

please help fr i don’t understand this

Answers

Answer:

A.    

   

Hope that helps!

Step-by-step explanation:

Answer:

the answer is A I believe good luck

This banana 8 inches How many 0.4 inch slices of banana can be cut from this banana?

Answers

Answer:

20 banna slices can be cut from a banna

Step-by-step explanation:

8 divided by 0.4 equals 20

20 slices

8 divided by 0.4 would give you an answer of 20 banana slices

i need to find the equations for these solutions

Answers

Answer:

hope these answers helps u out

Step-by-step explanation:

PLZZ MARK ME AS BRAINLIEST

I hope this helps you

Which of the following is equivalent?

Answers

I am not sure my fault

How do I find the volume of a solid by rotating the region bounded by the given curves about a specified line?

Answers

Step-by-step explanation:

if a region is bounded by two curves y=f(x) and y=g(x) on an internal a,b where 0<g(x)< f(x) then the volume of the solid obtained by the rotating region about the Y-axis is expressed by the integral of the difference of two functions: v= 2πbfax(x)jdx

A line passes through the points (1, 7) and (0, 3). What is its equation in slope-intercept form?

Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:1.  you can compute the slope, m

2.  point (0,3) is the y-intercept; b=33

3.  y = mx + b, so put the numerical values in for m & b.  DON

Step-by-step explanation:

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