find the limit as x approaches 0 of the function: (e^x.sinx)/x

Question

without using hopitals rule

Answer 1

e^x sin x / x

e^x --> 1+x + x^2/2! ....
sin x --> x -x^3/3! + x^5/5! ....
product--> x + x^2....
product/x --> 1 + x ...
---> 1 as x --> 0