I'm having a problem finding the limit when the function includes a trig function.
E.g. page 74,
#20 a, lim (x - 0) of 'sin x / (3sqrt(x))'
or
#20 b, lim (x - 0) of 'sin^2 x / x'
Any hints on how to tackle these ?

Question

I'm having a problem finding the limit when the function includes a trig function. 
E.g. page 74, 
#20 a, lim (x -> 0) of 'sin x / (3sqrt(x))'
or
#20 b, lim (x -> 0) of 'sin^2 x / x'
Any hints on how to tackle these ?

espex · Answer

You attack it in the same manner you would if it was x^2 or any other function of x. As you apply the limit you will end up taking the sin(0). Use a substitution variable if that helps during the rationalization of the numerator, then just place the trig function back afterwards.

jkristia · Answer

eSpecX, I'm not sure I understand your explanation, but I found some helpful videos on youtube taking limits of trig functions. The goal is to always get the equation into the form of either   sin x / x = 1   or   (1 - cos x) / x = 0. In the case of $$\sin x / 3\sqrt{x}$$ I should multiply by $$x / x$$ to get$$(x / 3)(\sin x / x) = (x / 3)(1) = 0/3 = 0$$
I think that is how it should be solved.