A community for students.
Here's the question you clicked on:
 0 viewing
Jusaquikie
 3 years ago
find the linear approximation of f(x)=sqrt 1x at a=0 and use it to approximate sqrt .98
Jusaquikie
 3 years ago
find the linear approximation of f(x)=sqrt 1x at a=0 and use it to approximate sqrt .98

This Question is Closed

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.0find the linear approximation of \[f(x)=\sqrt{1x}\] at a=0 and use it to approximate \[\sqrt{.98}\]

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.0i know f(x) = f(a)+f'(a)(xa) and f'(x) here is \[\frac{ 1 }{ 2\sqrt{1x} }\] so \[f'(a)= \frac{ 1 }{\sqrt{10} }=1\] so \[f(x)=\sqrt{10}+(\frac{ 1 }{ 2\sqrt{10} })(x0)\] so \[f(x)=1+(\frac{ 1 }{2 })x(\frac{ 1 }{2 })0 = 1\frac{ 1 }{2 }x\] \[f(.98)= 1\frac{ 1 }{ 2 }(.98)\] and i'm lost, so where did i go wrong and what should i do?

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.0\[f'(a)=\frac{ 1 }{2\sqrt{10} }=\frac{ 1 }{ 2 }\]i messed that up when i typed it but put it in the equation

Xetion
 3 years ago
Best ResponseYou've already chosen the best response.2I may be off here... but if linear approx of (1x)^0.5 is f(x) = 11/2*x Would you want to plug in 0.02 into the equation not 0.98. Because to get the square root of 0.98 is the same a (10.02)^0.5?

Xetion
 3 years ago
Best ResponseYou've already chosen the best response.2\[\sqrt{1x} \approx 1 \frac{ x }{ 2 }\] Therefore \[\sqrt{0.98} = \sqrt{1  0.02} \approx 1  \frac{ 0.02 }{ 2 }\]

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.0agree with him ^ put x=0.02.

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.0ok thanks i was confused because i was used to approximating using just square root of x and plugging in a value and taking the tangent line etc but the 1x through me and i wasn't sure how to show my work.

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.0in general, its good to know that \(\huge \sqrt[n]{1x} \approx 1nx\)

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.0\(\huge \sqrt[n]{1 \pm x} \approx 1 \pm nx\)
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.