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Math Help - limit of function.

  1. #1
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    limit of function.

    An incorrect use of L hospital rule is illustrated in the following limit computation.Explain what is wrong and find correct value of limit.
    lim x->pi/2 (sinx/x)= lim x->pi/2 (cosx/1)=0
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    \sin \left( {\frac{\pi }{2}} \right) = ?
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  3. #3
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    Hello, Bobby77!

    An incorrect use of L'Hopital's Rule is illustrated in the following limit computation.
    Explain what is wrong and find correct value of limit.

    \lim_{x\to\frac{\pi}{2}}\frac{\sin x}{x} \:= \:\lim_{x\to\frac{\pi}{2}}\frac{\cos x}{1}\:=\:0

    To apply L'Hopital's Rule, the function must approach an indeterminate form:
    . . \frac{0}{0},\;\frac{\infty}{\infty},\;0^0,\;\hdots

    This limit exists: . \lim_{x\to\frac{\pi}{2}}\frac{\sin x}{x} \;=\;\frac{\sin\left(\frac{\pi}{2}\right)}{\frac{\  pi}{2}} \;=\;\frac{1}{\frac{\pi}{2}} \;=\;\frac{2}{\pi}

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