Limits and Deri...

What is the value of \(\lim _{x \rightarrow 0} \frac{(1-\cos 2 x)^{2}}{x^{4}}\)?

Evaluate \(\underset{{{x \rightarrow 0}}}{\lim} \frac{x \tan x}{1-\cos x}\)

If \(\underset{{{{x} \rightarrow \infty}}}{\lim}\left(\frac{{x}^{2}+{x}+1}{{x}+1}-{px}-{q}\right)=-3\), then \({p}\) and \({q}\) is:

If \({y}=\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\ldots \infty}}}\), then \(\frac{{dy}}{{dx}}=?\)

Find the value of \(\lim _{\mathrm{x} \rightarrow 3} \frac{\mathrm{x}^{4}-81}{\mathrm{x}^{3}-27} \)

Let \(f(x)=\frac{1}{\sqrt{10-x^{2}}} \). What is the value of \(\lim _{x \rightarrow 1} \frac{{f}({x})-{f}(1)}{{x}-1}\)?

Find the value of \(k\) if \(\underset{{{x \rightarrow 7}}}{\lim} g(x)=k\) where \(g(x)=\sqrt{8 x-7}\)

Find the value of \(\underset{{{{x} \rightarrow \infty} }}{\lim}{x} \sin \left(\frac{\pi}{{x}}\right)\)

Find the value of \(\underset{{{x \rightarrow 0}}}{\lim} \frac{\tan 6 x+4 x}{4 x+\tan x}\)