Question

Limit as x approaches 0 of (tan3x^2+sin^25x)/x^2

Answer 1

`\displaystyle\lim_(x\to0)(\tan3x^2+\sin^25x)/(x^2)=\lim_(x\to0)\left((\sin3x^2)/(x^2\cos3x^2)+(\sin^25x)/(x^2)\right)`

`=\displaystyle3\left(\lim_(x\to0)(\sin3x^2)/(3x^2)\right)\left(\lim_(x\to0)\frac1{\cos3x^2}\right)+25\left(\lim_(x\to0)(\sin5x)/(5x)\right)^2`

`=3(1)(1)+25(1)^2`

`=28`