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Is this the same as lim x→2 sin(x)?

  1. Feb 29, 2016 #1
    1. The problem statement, all variables and given/known data
    if f(x)=sin(x), evaluate lim h→0 (f(2+h)-f(2))/h) to two decimal places

    2. Relevant equations
    (f(x+h)-f(x))/h

    3. The attempt at a solution
    On the assumption that this is the same as lim x→2 sin(x)
    sin(2)=0.91
     
  2. jcsd
  3. Feb 29, 2016 #2

    Mark44

    Staff: Mentor

    No, the limit at the top is not the same as sin(2).
     
  4. Feb 29, 2016 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Instead of "guessing" and remaining uncertain, try evaluating ##(f(2+h)-f(2))/h## numerically for a few small values of ##h##, such as ##h = 1/2,\, 1/4,\, 1/8, \ldots, ## etc. That way, you can answer your question for yourself and you will furthermore understand much better what is happening.
     
    Last edited: Feb 29, 2016
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