List of top Mathematics Questions on Limits asked in VITEEE

The distance of the point \( (-5, -5, -10) \) from the point of intersection of the line \[ r = -2i - j + 2k + \lambda(3i + 4j + 2k) \] and the plane \( r \cdot (i - j + k) = 5 \) is:

\[ \int_{\log \sqrt{n}}^{\log \sqrt{r}} 2x \sec^2\left( \frac{1}{3} \cdot 2x \right) \, dx \] is equal to:

Evaluate \( \lim_{x \to 2} \frac{\sqrt{x+7} - 3}{\sqrt{x-3} - 2} \):

The value of \[ \lim_{x \to 0} \frac{x^3 \cot x}{1 - \cos x} \] is:

The no. of points of discontinuity of the function f (x) = x - [x] in the interval (0, 7) are

\[ \lim_{x \to \infty} \frac{x^2}{3x - 3} = ? \]

At \( t = 0 \), the function \( f(t) = \sin \frac{t}{t} \) has

The limit of \( \int \frac{1}{\cos x} dx \) as \( b \to 0 \) is

The value of \[ \lim_{x \to \infty} \left( \frac{\pi}{2} - \tan^{-1} x \right)^{1/x} \] is:

The values of constants \( a \) and \( b \), so that \[ \lim_{x \to \infty} \left( \frac{x^2 + 1}{x + 1} - ax - b \right) = 0 \] are:

Find the value of the limit \[ \lim_{x \to 0} \frac{\sqrt{1 - \cos x}}{x} \]

If \(f:\mathbb{R}\rightarrow \mathbb{R}\) is defined by
\[ f(x)= \begin{cases} \dfrac{2\sin x-\sin 2x}{2x\cos x}, & x\neq 0 \\ a, & x=0 \end{cases} \] then the value of \(a\) so that \(f\) is continuous at \(0\) is

Evaluate
\[ \lim_{x\to 0}\left(\frac{x+5}{x+2}\right)^{x+3} \]

If \(g(x)\) is a polynomial satisfying \(g(x)g(y)=g(x)+g(y)+g(xy)-2\) for all real \(x\) and \(y\) and \(g(2)=5\), then \(\lim_{x\to 3} g(x)\) is

The value of \(f(0)\) so that \(\frac{-e^x+2^x}{x}\) may be continuous at \(x=0\) is