Limits and Deri...

The value of \(\underset{{{x \rightarrow 0}}}{\lim} \frac{\tan ^{2} 3 x}{x^{2}}\) is:

If \(y=x^{4}\left(x^{3}+2 x^{2}+5\right)\), then find \(y'\).

If \(y=\frac{4+3 x^{3}}{6 x^{4}}\), then find the value of \(\frac{d y}{d x}\).

Find the value of \(\lim _{{x} \rightarrow 5} \frac{{x}^{2}-25}{{x}^{2}-2 {x}-10}\)

If \(f(x)=x^{3}+3 x^{2}+3 x-7\), then find the value of \(\frac{d f(x)}{d x}\) at \(x=2\).

What is the value of \(\underset{{{{x} \rightarrow 0}}}{\lim} \frac{(1-\cos 2 {x})^{3}}{{x}^{6}}\)?

The value of \(\lim _{x \rightarrow 0} \frac{\cos 4 x-1}{1-\cos x}\) is:

Find the value of \(\lim _{{x} \rightarrow \infty} \frac{{x}^{4}+3 {x}^{2}+5}{{x}^{4}+{x}^{2}-6}\)