List of top Mathematics Questions on Limits asked in KEAM

Let $f(x) = \frac{(\sqrt{x}+3)(\sqrt{x}-1)}{x - 1}$ for $x \neq 1$. Then $\lim_{x \to 1} f(x)$ is equal to

Evaluate \( \lim_{x \to 1} \frac{\sqrt{x+3} \cdot \sqrt{x-1}}{x-1} \)

Evaluate the following limit: $ \lim_{x \to 0} \frac{1 + \cos(4x)}{\tan(x)} $

Find the limit: $ \lim_{x \to 0^+} 2 \left\lfloor x \right\rfloor - \frac{x}{|x|} $

Find the limit: $ \lim_{x \to 0^+} 2 \left\lfloor x \right\rfloor - \frac{x}{|x|} $

Find the limit: $ \lim_{x \to 11} \frac{x - 11}{\sqrt{49 + x^2} - 13} $

Evaluate the following limit: $ \lim_{\theta \to 0} \frac{\theta \sin 2\theta}{1 - \cos 2\theta} $

If \(f(x) =   \begin{cases}     x^2\sin(\frac{\pi}{6}x)       & for\ x\leq-3 \\      x\cos(\frac{\pi}{3}x)       & for\ x\gt-3   \end{cases}\), then the value of \(\displaystyle\lim_{x\rightarrow3}f(x)\ is\ equal\ to\)

If \(f(x) =   \begin{cases}  e^x, & \text{if}\ x\leq1 \\  mx+6, & \text{if}\ x\gt1 \end{cases}\) be differentiable at x=1. Then the value of m is

If \(f(x) =   \begin{cases}  3x+2, & \text{if}\ x\lt-2 \\  x^2-3x-1, & \text{if}\ x\geq-2 \end{cases}\). Then \(\lim\limits_{x\rightarrow2^-}f(x)\) and \(\lim\limits_{x\rightarrow2^+}f(x)\) are respectively

\(\lim\limits_{t\rightarrow0}\frac{\sin2t}{8t^2+4t}\) is equal to

$\lim_{x \to \infty} \frac{3x^3 + 2x^2 - 7x + 9 }{4x^3 + 9x - 2 }$ is equal to

If $f(x) = \frac{x+2}{3x-1}$, then $f(f(x))$ is:

$\lim_{x \to 0} \frac{\log(1 + 3x^2)}{x(e^{5x} - 1)} =$

Let \( f(x) = (x^5 - 1)(x^3 + 1) \), \( g(x) = (x^2 - 1)(x^2 - x + 1) \) and let \( h(x) \) be such that \( f(x) = g(x)h(x) \). Then \( \lim_{x \to 1} h(x) \) is:

Let \( f(x) = (x^5 - 1)(x^3 + 1) \), \( g(x) = (x^2 - 1)(x^2 - x + 1) \) and let \( h(x) \) be such that \( f(x) = g(x)h(x) \). Then \( \lim_{x \to 1} h(x) \) is:

\( \lim_{x \to 0} \frac{\log(1 + 3x^2){x(e^{5x} - 1)} = \)}

If \( f(x) = \frac{x+2{3x-1} \), then \( f(f(x)) \) is:}

Let \( f(x) = (x^5 - 1)(x^3 + 1) \), \( g(x) = (x^2 - 1)(x^2 - x + 1) \) and let \( h(x) \) be such that \( f(x) = g(x)h(x) \). Then \( \lim_{x \to 1} h(x) \) is:

\( \lim_{x \to 0} \frac{\log(1 + 3x^2){x(e^{5x} - 1)} = \)}

If \( f(x) = \frac{x+2{3x-1} \), then \( f(f(x)) \) is:}

The value of $\displaystyle \lim_{x \to 3} \frac{x^{5}-3^{5}}{x^{8}-3^{8}}$ is equal to