List of top Mathematics Questions on Limit and Continuity asked in IPU CET

The value of the limit as $x$ approaches $0$ for $\frac{\sin(5x){x}$ is}

The value of \[ \lim_{x \to 0} \int_0^x \sec^2 t \, dt \] is:

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If $ f(x) = [x \sin n\pi x] $, then which of the following is incorrect?

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The limit \[ \lim_{x \to 0} \frac{1 - \cos 2x}{x \tan 4x} \]

If \[ f(x) = \begin{cases} \frac{1 - \sin x}{(n - 2x)^2} & \text{if} \quad x \neq \frac{\pi}{2} \log (\sin x) \cdot \log \left( 1 + \frac{\pi}{4x + x^2} \right) & \text{if} \quad x = \frac{\pi}{2} \end{cases} \] is continuous at $ x = \frac{\pi}{2} $, then $ k $ is equal to

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The value of $\lim_{x \to a} \frac{\log x - 1}{x - a}$ is equal to

Choose the most appropriate option. \[ \lim_{x \to 1} \sin(x - 1) \cdot \tan\left( \frac{\pi}{x} \right) \]

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\[ \lim_{x \to 0} \frac{\ln \cos 2x}{\sin 2x} \]

\[ \lim_{x \to 0} \frac{\sqrt{1+x} - \sqrt{1 - x}}{x} \]