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

suju101

test the differentiability of the function at x=0 F(x)= {x*sin(1/x)if x≠0 and 0 if x=0

  • 2 years ago
  • 2 years ago

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

    It is not differentiable. you can check that the function is continous. Applyinf frist principle \[f \prime(0)=\lim_{h \rightarrow 0}(f(h)-f(0))/h=hsin(1/h)/h=\sin1/h\] sin1/h is undefined as h tends to 0 hence it is not differentiable.

    • 2 years ago
  2. suju101
    Best Response
    You've already chosen the best response.
    Medals 0

    but can't we say 1/h->infinity

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

    Yeah since 1/h->infinty the limit sin(1/h) and subsequently f'(0) is undefined.

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

    If you have x^a sin(1/x) it is differentiable at x=0 only for a>1 for an integer a am not sure for fractional a value.

    • 2 years ago
  5. JamesJ
    Best Response
    You've already chosen the best response.
    Medals 1

    The derivative exists at x=0 if the limit of the difference quotient \[ \frac{f(h) - f(0)}{h} = \sin(1/h) \] as h -> 0 exists. But it doesn't exist because \[ \lim_{h \rightarrow 0} \sin(1/h) \] doesn't exist. Instead, as h approaches 0, from either above or below, sin(1/h) oscillates faster and faster between -1 and 1. If it had a limit, L say, then we could make sin(1/h) as close as we liked to L by making h sufficiently close to zero. But on the contrary, for any restriction of h close to zero, sin(1/h) assumes infinitely many values between -1 and 1.

    • 2 years 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.