Question

lim x→0+ sin x ln 2x

Answer 1

this is indeterminate form 0*infinity so you want to get it in the form that you can use l'hopitals theorem ie. (sinx)/(1/ln2x) which is indeterminate of the form 0/0 so l'hopitals theorem can be used

Answer 2

If we rewrite it a little, we might get:\[\frac{\ln(2x)}{\csc(x)}\] and approaching that from the positive side suggests an "Indeterminate Form" or the type \[\frac{ \infty }{ \infty }\]. Can you do anything with that?

Answer 3

yes, thanks!