A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
Find the linearization, say L(x)=ax+b, of fx=sin^(2)x at the point x=pi/4
anonymous
 5 years ago
Find the linearization, say L(x)=ax+b, of fx=sin^(2)x at the point x=pi/4

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hi Lifesaver, You have to take a Taylor series expansion about pi/4 for sin^2(x) and truncate after the first two terms. So, \[f(x)=\sum_{k=0}^{\infty}[f^k(x_0)/k!](xx_0)^k\] Set \[x_0=\pi/4\] and truncate after k=1 (i.e. sum up only the first two terms, k=0 and k=1). In this instance, \[\sin^2(x)=\sin^2(x_0)+2\sin(x)\cos(x)(xx_0)+...\] so that, \[\sin^2(x)=\sin^2(\pi/4)+2\sin(\pi/4)\cos(\pi/4)(x\pi/4)+...\] After truncating the above (i.e. dropping everything after the term 2sin(x)cos(x)(xx_0), and finding values for sin(pi/4), cos(pi/4), etc., you have what you're looking for, \[L(x)=x+(1/2\pi/4)\] as a linear approximation to sin^2(x) about the point pi/4. I hope I've interpreted your question correctly.
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.