Limits, Continuity and Differentiability PYQs - Last 5 Years
VITEEE / Mathematics / Calculus / 11 recent questions
MathematicsCalculus2021-2025
Practice 11 VITEEE Mathematics questions from Limits, Continuity and Differentiability. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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Mathematics / Calculus
2021-2025
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2021-2025
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2016-2025
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11 in last 5 years11 in last 10 years
Last 5 Years Limits, Continuity and Differentiability Questions
Showing 11 of 11 filtered questions.
1Limits Continuity And Differentiability
If $f(x)=\left(\frac{x^2+5 x+3}{x^2+x+2}\right)^x$, then $\lim _{x \rightarrow \infty} f(x)$ is
MCQ+4 / -12025
2Limits Continuity And Differentiability
$\lim _\limits{x \rightarrow 0} \frac{1}{x} \int_0^x(1+\sin 3 t)^{\frac{1}{t}} d t$ is equal to
MCQ+4 / -12024
3Limits Continuity And Differentiability
$\lim \limits_{x \rightarrow 0} \frac{\sin \left(\pi \cos ^2 x\right)}{x^2}$ equal to
MCQ+4 / -12024
4Limits Continuity And Differentiability
For \(x \in R, f(x)=|\log 2-\sin x|\) and \(g(x)=f(f(x))\), then
MCQ+4 / -12023
5Limits Continuity And Differentiability
If $$f(x)=\left\{\begin{array}{cc}(\sin x+\cos x)^{\operatorname{cosec} x} & ,-\frac{\pi}{2}< x<0 \\ a & ,x=0 \\ \frac{e^{1 / x}+e^{2 / x}+e^{3 / x}}{a e^{-2+\frac{1}{x}}+b e^{-1+\frac{3}{x}}} & , 0< x<\frac{\pi}{2}\end{array}\right.$$ is c...
MCQ+4 / -12022
6Limits Continuity And Differentiability
The value of \(\lim _\limits{t \rightarrow \infty} \frac{\ln \left(\frac{3}{2} t\right)}{t^2}\)
MCQ+4 / -12022
7Limits Continuity And Differentiability
The value of
\(\lim _\limits{x \rightarrow \infty}\left[\frac{p^{1 / x}+q^{1 / x}+r^{1 / x}+s^{1 / x}}{4}\right]^{3 x}, p, q, r, s>0 \text {, }\) is
\(\lim _\limits{x \rightarrow \infty}\left[\frac{p^{1 / x}+q^{1 / x}+r^{1 / x}+s^{1 / x}}{4}\right]^{3 x}, p, q, r, s>0 \text {, }\) is
MCQ+4 / -12022
8Limits Continuity And Differentiability
The value of \(f(x) = \mathop {\lim }\limits_{x \to 2} {{{x^3} - 3{x^2} + 4} \over {{x^4} - 7x - 2}}\)
MCQ+4 / -12022
9Limits Continuity And Differentiability
\(\lim _\limits{x \rightarrow 0}\left\{\tan \left(\frac{\pi}{4}+x\right)\right\}^{1 / x}\) is equal to
MCQ+4 / -12021
10Limits Continuity And Differentiability
The value of \(\lim _\limits{n \rightarrow \infty}\left\{\frac{1+2+3+\ldots+n}{n+2}-\frac{n}{2}\right\}\) is
MCQ+4 / -12021
11Limits Continuity And Differentiability
If $$f(x)=\left\{\begin{array}{cc}\frac{(1-\cos 4 x)}{x^2}, & \text { if } x < 0 \\ a, & \text { if } x=0, \\ \frac{\sqrt{x}}{\sqrt{(16+\sqrt{x})}-4}, & \text { if } x > 0\end{array}\right.$$ then \(f(x)\) is continuous at \(x=0\), for $$a$...
MCQ+4 / -12021