Limit as x approaches 0 of (2x+Sinx)÷(x)

Question

Evaluate analytically.

Answer 1

you want lim, as x approaches zero, of [2 + (sin x)/x] which is 1 + 1 = 3.

 

The llimit at 0 of (sin x)/x is a well known fact developed early in Calculus I.

Answer 2

Lim_x->0(2x+sin x)/x=lim_x-->0(2+(sin x)/x)=2+lim_x-->0(sin x)/x=2+1=3.