# Calc

I have a test soon.. and I really need to know how to do this problem.. please help!!!

lim as x-->0 sin^2(x)/tan(x^2)

the answer is 1, but I have no clue how to get that!

Use series expansions. Look up Taylor expansion on google and study that topic first.

Using series expansion techniques these limit problems become pretty trivial. For x in a neighborhood of zero:

Sin(x) = x + O(x^3) ---->

sin^2(x) = x^2 + O(x^4)

tan(x) = x + O(x^3) -->

tan(x^2) = x^2 + O(x^6)

And you see that:

sin^2(x)/tan(x^2) = 1 + O(x^4)

So, the limit is 1

1. 👍
2. 👎
3. 👁

## Similar Questions

1. ### Math

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Find the measure of x in the triangle. Show all your work. This is for the connexus test Essential Tools of Geometry Unit

2. ### Algebra

1. Find the surface area for the given prism. ( 1 point ) - 7,154 ft^2 2,624 ft^2 9,778 ft^2 8,432 ft^2 I don't want the answers to the whole test, I been trying to maintain good grades but I haven't been learning anything. Any

3. ### Math

For questions 4–5, use the following two ways to display the test scores received on Mr. Alexander's math test. Use these displays to solve each problem. Stem | Leaf 6 | 8 9 7 | 0 3 5 8 9 8 | 1 2 2 5 7 8 8 9 9 | 0 2 3 Pie Chart:

4. ### Geometry

I missed this problem on my test. I had 23 ft and the correct answer was 16 ft. How should I of worked this problem? A trapezoid has base lengths of 8.5 and 14.5 feet with the area of 184 square feet. What is the height of the

1. ### chemistry

This question I really don't get it. I tried tried tried to figure out how to start solve the problem but still couldn't figure out. So can you help me with one question PLEASE? If so, can you please explain to me how you get the

2. ### algebra

I am having trouble anwering the following problem: The test scores from Mrs. Gray's math class are shown below. 72, 73, 66, 71, 82, 85, 86, 89, 91, 92 Construct a box-and-whisker plot to display this data. I don't know how to

3. ### Maths

I got 30% on a 10-problem test, 70% on a 20-problem test and 80% on a 30-problem test. If the three tests are combined in one 60-problem test what percentage is my overall score?

4. ### mathematics

Jake correctly answered 15 out of 25 questions in Test 1 and 18 out of 25 questions on test 2. On Test 3 he missed 5 out of 27 questions. Which test had the best score? A) Test 2 and Test 3 B) Test 2 C) Test 3 D) Test 1 ??

1. ### Calculus

PLEASE HELP ME!!! Give explanation too! Thank you so much! Match each series to the test that should be used to test for convergence/divergence. While it is possible that each test could apply to more than one series, in this

2. ### Statistics

When population data are discrete and you want to compare two populations, which test is most appropriate? a. T-test b. Anderson Darling c. Leven’s d. 2-Proprotion test e. F-test

3. ### math

The stem-and-leaf plot shows the test scores of a science class. How many students scored 78? science test scores 6: 8,8,9 7:2 ,5,5,5,8,8,8,8,9 8: 2,2,2,6,6,9,9 9: 0,0,0,2,2,5,5,5 key: 8/2 or 8 and 2 means 82 is the answer 1 or 2

4. ### statistics

Which of the following is NOT a required step for a significance test? (a) State null and alternative hypothesis in the context of the problem. (b) Identify the test to be used and justify the conditions for using it. (c) State