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Thread: evaluating limits with trig functions

  1. February 8th 2009, 09:10 PM #1
    calcbeg
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    evaluating limits with trig functions

    Hi

    I am on my last question so hopefully someone is still out there to help me!

    Question says "evaluate the following limits"

    First

    lim x/tan x
    x->0

    Second

    lim x2/(1-cos^2 x)
    x_>0

    I can't seem to find any examples of how to do either of these.

    Thanks in advance
    this calculus beginner
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  2. February 8th 2009, 09:18 PM #2
    Abu-Khalil
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    \lim_{x\to 0}\frac{x}{\tan x}=\lim_{x\to 0}\underbrace{\frac{x}{\sin x}}_{\to 1}\underbrace{\cos x}_{\to 1}=1.

    \lim_{x\to 0}\frac{x^2}{1-\cos^2 x}=\lim_{x\to 0}\frac{x^2}{\sin^2 x}=\lim_{x\to 0}\left(\frac{x}{\sin x}\right)^2=1^2=1.
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