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.
#2) Use quotient rule [tex]\frac{f'g - fg'}{g^2}[/tex] Remember for solving log equations: [tex]e^{ln x} = x[/tex]
#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 [tex]tan(2x) = \frac{2tan x}{1-tan^2 x} [/tex] 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.
