hiiii.. please help me with this limit question ​

Answer:

π

Step-by-step explanation:

Solving without L'Hopital's rule:

lim(x→0) sin(π cos²x) / x²

Use Pythagorean identity:

lim(x→0) sin(π (1 − sin²x)) / x²

lim(x→0) sin(π − π sin²x) / x²

Use angle difference formula:

lim(x→0) [ sin(π) cos(-π sin²x) − cos(π) sin(-π sin²x) ] / x²

lim(x→0) -sin(-π sin²x) / x²

Use angle reflection formula:

lim(x→0) sin(π sin²x) / x²

Now we multiply by π sin²x / π sin²x.

lim(x→0) [ sin(π sin²x) / x² ] (π sin²x / π sin²x)

lim(x→0) [ sin(π sin²x) / π sin²x] (π sin²x / x²)

lim(x→0) [ sin(π sin²x) / π sin²x] lim(x→0) (π sin²x / x²)

π lim(x→0) [ sin(π sin²x) / π sin²x] [lim(x→0) (sin x / x)]²

Use identity lim(u→0) (sin u / u) = 1.

π (1) (1)²

π

Solving with L'Hopital's rule:

If we plug in x = 0, the limit evaluates to 0/0.  So using L'Hopital's rule:

lim(x→0) [ cos(π cos²x) (-2π cos x sin x) ] / 2x

lim(x→0) [ -π cos(π cos²x) sin(2x) ] / 2x

-π/2 lim(x→0) [ cos(π cos²x) sin(2x) ] / x

Again, the limit evaluates to 0/0.  So using L'Hopital's rule one more time:

-π/2 lim(x→0) [ cos(π cos²x) (2 cos(2x)) + (-sin(π cos²x) (-2π cos x sin x)) sin(2x) ] / 1

-π/2 lim(x→0) [ 2 cos(π cos²x) cos(2x) + π sin(π cos²x) sin²(2x) ]

-π/2 (-2)

π

please help 22 points

Answer correctly for brainliest

PLEASE HELP!! PLEASE STEP BY STEP!

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A. A sixth grader wants to raise less than $317 for a fundraiser, and she has already raised $111.

B. A sixth grader wants to raise more than $317 for a fundraiser, and she has already raised $111.

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I do give brainliest

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(Non-fat, Low-fat, Lemon, Banana)

BRAINLIEST FOR CORRECT ANSWER + 17 points

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Which of the following statements is true about the three quadrilaterals?

1. M and O are similar and congruent.

2. O and N are similar and congruent.

3. M and N are similar but not congruent.

4. M and O are similar but not congruent.

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Graph with x axis labeled game levels and y axis labeled gems collected. A line begins at 0 comma 0 and goes through points 6 comma 450 and 8 comma 600.

p equals 2 over 150

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p = 75

p = 150

Answer and explanation?

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Someone, Please help!
The page is in the file.

PLS I NEED HELP ITS DUE TODAY

I NEED THIS RIGHT NOW

Can you please help fast

Can Someone Help Me Please? I am offering 100 points!
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Draw a closed circle at 6.
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Shade all numbers greater than 6.
Shade all numbers to the right of 6.
Shade all numbers to the left of 6.

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