[tex]\displaystyle\lim_{x\to0}\frac{\tan3x^2+\sin^25x}{x^2}=\lim_{x\to0}\left(\frac{\sin3x^2}{x^2\cos3x^2}+\frac{\sin^25x}{x^2}\right)[/tex]
[tex]=\displaystyle3\left(\lim_{x\to0}\frac{\sin3x^2}{3x^2}\right)\left(\lim_{x\to0}\frac1{\cos3x^2}\right)+25\left(\lim_{x\to0}\frac{\sin5x}{5x}\right)^2[/tex]
[tex]=3(1)(1)+25(1)^2[/tex]
[tex]=28[/tex]
