A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
4x^2 tan^−1(9x^3) could someone show me how to represent this as a maclaurin series
anonymous
 3 years ago
4x^2 tan^−1(9x^3) could someone show me how to represent this as a maclaurin series

This Question is Closed

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0First you find the MacLaurin series for tan^1(u), then you substitute u=9x^3 in each term, then you multiply each term by 4x^2. To deal with tan^1(u), deal with its derivative, which is 1/(1+u^2), then when you're done, integrate each term. So, how to find the Series for 1/(1+u^2)? One trick is to substitute t =  (u^2), so it becomes 1/(1  t). You should recognize this as the solution to the simple power series: 1 + t + t^2 + t^3 + … Putting back the u’s in place of the t’s we get: 1 – u^2 + u^4 – u^6 + … Integrating each term gives: tan^1(u) = u – u^3/3 + u^5/5 – u^7/7 + … Substituting back for u=9x^3 gives: tan^1(9x^3) = 9x^3 – 9^3(x^9)/3 + 9^5(x^15)/5  9^7(x^21)/7 + … And finally multiplying by 4x^2, we get the final aswer: 4x^2 tan^1(9x^3) = (4)(9)(x^5) – (4)(9^3)(x^11)/3 + (4)(9^5)(x^17)5 – (4)(9^7)(x^23)/7 + … Better check the math – I might have messed up in detail, but the general approach should be correct.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.