find the limit

Question

find the one sided limit at the point x=0 for function

f(x)={sinx/x, x>0 ; x+1, x≤0

Answer 1

Dona,

         The intuitive way to find the limit is to expand sin(x) in a power series around 0, i.e. sin(x)≈x-x³+x⁵/120+.....for x near 0.

so sin(x)/x≈1-x²+x⁴/120+.... we can now take the limit lim_x→0sin(x)/x=1. QED :)

 

Hope this helps

 

Jim