Calculus L'Hôpital's Rule?
Apply L'Hôpital's Rule to evaluate the following limit. It may be necessary to apply it more than once.
lim_{x to\pi/2} {\sin\(x+\pi }/{2}\) / cos(x+pi)} =
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Apply L'Hôpital's Rule to evaluate the following limit. It may be necessary to apply it more than once.
lim_{x to\pi/2} {\sin\(x+\pi }/{2}\) / cos(x+pi)} =
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lim [ sin(x + π/2) / cos(x + π) ]
x -> π/2
is an indeterminate form 0/0 , so applying L'Hopital's rule by differentiating numerator and denominator separately, the limit
= lim [ cos(x + π/2) / - sin(x + π) ]
...x -> π/2
= cos(π) / (- sin(3π/2))
= -1 / (- (-1))
= -1 / 1
= -1