Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Jusaquikie

  • 2 years ago

find the linear approximation of f(x)=sqrt 1-x at a=0 and use it to approximate sqrt .98

  • This Question is Closed
  1. Jusaquikie
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    find the linear approximation of \[f(x)=\sqrt{1-x}\] at a=0 and use it to approximate \[\sqrt{.98}\]

  2. Jusaquikie
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i know f(x) = f(a)+f'(a)(x-a) and f'(x) here is \[\frac{ -1 }{ 2\sqrt{1-x} }\] so \[f'(a)= \frac{ -1 }{\sqrt{1-0} }=-1\] so \[f(x)=\sqrt{1-0}+(\frac{ -1 }{ 2\sqrt{1-0} })(x-0)\] 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?

  3. Jusaquikie
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[f'(a)=\frac{ -1 }{2\sqrt{1-0} }=-\frac{ 1 }{ 2 }\]i messed that up when i typed it but put it in the equation

  4. Jusaquikie
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @hartnn Help please

  5. Xetion
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I may be off here... but if linear approx of (1-x)^0.5 is f(x) = 1-1/2*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 (1-0.02)^0.5?

  6. Xetion
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\sqrt{1-x} \approx 1- \frac{ x }{ 2 }\] Therefore \[\sqrt{0.98} = \sqrt{1 - 0.02} \approx 1 - \frac{ 0.02 }{ 2 }\]

  7. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    agree with him ^ put x=0.02.

  8. Jusaquikie
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok 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 1-x through me and i wasn't sure how to show my work.

  9. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    in general, its good to know that \(\huge \sqrt[n]{1-x} \approx 1-nx\)

  10. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \(\huge \sqrt[n]{1 \pm x} \approx 1 \pm nx\)

  11. Not the answer you are looking for?
    Search for more explanations.

    Search OpenStudy
    • Attachments:

Ask your own question

Ask a Question
Find 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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.