List of top Mathematics Questions on limits and derivatives asked in JKCET

The value of $ \displaystyle\lim_{x\to\infty} \left(\frac{x+5}{x+2}\right)^{x} $ is equal to
$ \underset{x\to 0}{\mathop{\lim }}\,\,\frac{\sin {{x}^{2}}}{1-\cos x} $ is
Find $ \frac{dy}{dx}, $ if $ y={{\sin }^{2}}x+{{\cos }^{4}}x $
Find the derivative of $ \sqrt{2}x+2\sqrt{x}-\frac{1}{x} $ ?
$ \underset{x\to 0}{\mathop{\lim }}\,\,{{\left\{ \tan \left( \frac{\pi }{4}+x \right) \right\}}^{1/x}} $ is equal to
$ \underset{n\to \infty }{\mathop{\lim }}\,\,\,\frac{{{2}^{n+1}}+{{3}^{n+1}}}{{{2}^{n}}+{{3}^{n}}} $ is equal to
$ \underset{x\to 0}{\mathop{\lim }}\,\frac{1}{x}{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right) $ =