Question

How to calculate this? `lim_(x->0)(ln(1+7x^2)/(7x^2)-ln(1+2x)/(2x))`;`x>0`.

Answer 1

`0`

Explanation:

First, we know that `log_e(1) = 0` and also

`lim_(x->0)(log_e(1+x)-log_e(1))/x = d/(dx)log x]_(x = 1) = 1`

so

`lim_(x->0)(ln(1+7x^2)/(7x^2)-ln(1+2x)/(2x)) = d/(dx)log_e(1) -d/(dx)log_e(1)=1-1=0`