Question

I am studying for a Calculus test and have the answers for the study guide but I'm having trouble with problems 2, 3, 4 (finding maximums and minimums for each) as well as #9 (computing the limit). The answers are written next to each question.

Answer 1

#2) Use quotient rule
$\frac{f'g - fg'}{g^2}$
Remember for solving log equations:
$e^{ln x} = x$

#3) Derivative of tan = sec^2 = 1/cos^2
Domain of tan is [-pi/2, pi/2], only consider x values in that domain.

#4 Use Quotient rule

#9  Use double angle identity for tan
$tan(2x) = \frac{2tan x}{1-tan^2 x}$
This way you can rewrite tan(pi/2) in terms of tan(pi/4).
Next use L'hopitals rule, which says the limit of indeterminate form(0/0) equals limit of quotient of derivatives of top/bottom of fraction.

Take derivative of both top part and bottom part separately, then reevaluate the limit. <span />