Question

lim x->0 (x^2(3+sinx))/(x+sinx)^2)

Answer 1

without using l'hospital's rule

Answer 2

\[\lim_{x \rightarrow 0}\frac{x^2(3+\sin(x))}{(x+\sin(x))^2}\]
\[\lim_{x \rightarrow 0}\frac{3x^2+x^2\sin(x)}{x^2+2x \sin(x)+\sin^2(x)}\]
\[\lim_{x \rightarrow 0}\frac{3x^2+x^2\sin(x)}{x^2+2x \sin(x)+\sin^2(x)} \frac{x^2}{x^2}\]
\[\lim_{x \rightarrow 0}\frac{3+\sin(x)}{1+2 \frac{\sin(x)}{x}+(\frac{\sin(x)}{x})^2}\]
\[\frac{3+0}{1+2(1)+(1)^2}\]

Answer 3

i divided the top by x^2
and i divided the bottom by x^2