Question

Find the limit of the function lim x->0 (sinx/x)^sinx/x-sinx

a:e^-1

b:1

c:e

d:+infinity

Answer 1

Using L hopitals rule ,

lim x->0 $e^{\frac{sinx}{x-sinx}ln\frac{sinx}{x}}$

limx->0${e^{ln\frac{sinx}{x}}}$ $e^{\frac{sinx}{x-sinx}}$

limx->0 ${e^{ln\frac{sinx}{x}}}$limx->0 $e^{\frac{sinx}{x-sinx}})$

1*infinity= infinity