Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

jkristia

Problem 5A-3g, is the answer correct?

  • 10 months ago
  • 10 months ago

  • This Question is Closed
  1. jkristia
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm not able to get the same nice clean answer as in the solution, and I think the problem is a mistake in the given solution where he get \[\frac{dy}{dx} \frac{x}{\sqrt{1 - x^2}} = (1-x^2)^{-3/2} ??\] it seems like he forgot the \(x\) in the numerator I get \[=\frac{-x^2+x+1}{(1-x^2)\sqrt{1-x^2}}\] What am I missing, where is my mistake ?

    • 10 months ago
  2. OBMD
    Best Response
    You've already chosen the best response.
    Medals 1

    First change the equation to \[\frac{ dy }{ dx}x(x-x ^{2})^{-\frac{ 1 }{ 2 }}\] Use the product rule you get \[(1)(1-x ^{2})^{-\frac{ 1 }{ 2 }}+x(-\frac{ 1 }{ 2 })(1-x ^{2})^{-\frac{3 }{ 2 }}(-2x)\] this can be simplified to \[\frac{ 1-x ^{2} }{(1-x ^{2})^{\frac{3}{2}} }+\frac{ x ^{2} }{(1-x ^{2})^{\frac{3}{2}} }\] which equals \[\frac{ 1 }{ (1-x ^{2} )^{\frac{ 3 }{ 2 }}}\] or\[(1-x ^{2})^{\frac{ -3 }{ 2 }}\]

    • 10 months ago
  3. OBMD
    Best Response
    You've already chosen the best response.
    Medals 1

    Note that \[(1-x ^{2})^{-\frac{ 1 }{ 2 }}=\frac{ 1 }{ (1-x ^{2})^{\frac{ 1 }{ 2 }} }=\frac{ 1-x ^{2} }{ (1-x ^{2})^{ \frac{ 3 }{ 2 } }}\]

    • 10 months ago
  4. jkristia
    Best Response
    You've already chosen the best response.
    Medals 0

    oh man.... you are right :). I have to go back and check my calculation, but I think my silly mistake was to multiply by (-2), not (-2x), arghhh... sometime you just go blind staring at a problem.

    • 10 months ago
    • Attachments:

See more questions >>>

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.