Question

Evaluate the limit lim x—->0 sin(2x)/x^2+x

Answer 1

Recall that

`\displaystyle\lim_(x\to0)(\sin ax)/(ax)=1`

for
`a\\eq0`.

We have

`\displaystyle\lim_(x\to0)(\sin2x)/(x^2+x)=\lim_(x\to0)(\sin2x)/(2x)\cdot\lim_(x\to0)\frac2{x+1}=2`