Limits, Continuity and Differentiability PYQs - Last 5 Years
BITSAT / Mathematics / Calculus / 10 recent questions
MathematicsCalculus2021-2025
Practice 10 BITSAT 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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2021-2025
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Last 5 Years Limits, Continuity and Differentiability Questions
Showing 10 of 10 filtered questions.
1Limits Continuity And Differentiability
If $\mathop {\lim }\limits_{x \to \infty }\left\{\frac{x^2-1}{x+1}-a x-b\right\}=2$. The value of $a$ is
MCQ+3 / -12025
2Limits Continuity And Differentiability
Consider the function $g(x)$ defined as
$$ g(x)=\left\{\begin{array}{cc} \frac{x^2-4}{x^2-2|x-2|-4}, & x \neq 2 \\ \frac{3}{4}, & x=2 \end{array}\right. $$
Which of the following statements is true about the continuity of $g(x)$ ?
$$ g(x)=\left\{\begin{array}{cc} \frac{x^2-4}{x^2-2|x-2|-4}, & x \neq 2 \\ \frac{3}{4}, & x=2 \end{array}\right. $$
Which of the following statements is true about the continuity of $g(x)$ ?
MCQ+3 / -12025
3Limits Continuity And Differentiability
The value of $\lim _{x \rightarrow \frac{\pi}{2}} \frac{\cot x-\cos x}{(\pi-2 x)^3}$ is
MCQ+3 / -12025
4Limits Continuity And Differentiability
Let $ f $ be the function defined by$ f(x)=\left\{\begin{array}{cc} \frac{x^{2}-1}{x^{2}-2|x-1|-1}, & x \neq 1 \\ \frac{1}{2}, & x=1 \end{array}\right. $
MCQ+3 / -12024
5Limits Continuity And Differentiability
\(\text { The value of } \lim _\limits{x \rightarrow 0} \frac{(27+x)^{1 / 3}-3}{9-(27+x)^{2 / 3}} \text { equals to }\)
MCQ+3 / -12023
6Limits Continuity And Differentiability
The value of \(\lim _\limits{x \rightarrow 0} \frac{8}{x^8}\left(1-\cos \frac{x^2}{2}-\cos \frac{x^2}{4}+\cos \frac{x^2}{2} \cos \frac{x^2}{4}\right)\) is
MCQ+3 / -12023
7Limits Continuity And Differentiability
The value of \(\mathop {\lim }\limits_{x \to 0} {{{{(1 + x)}^{{1 \over x}}} - e + {1 \over 2}ex} \over {{x^2}}}\) is
MCQ+3 / -12022
8Limits Continuity And Differentiability
The value of \(\mathop {\lim }\limits_{x \to 0} {{1-\cos (1 - \cos x)} \over {{x^4}}}\) is
MCQ+3 / -12022
9Limits Continuity And Differentiability
If \(f(x) = \left\{ {\matrix{
{a{x^2} + 1,} & {x \le 1} \cr
{{x^2} + ax + b,} & {x > 1} \cr
} } \right.\) is differentiable at x = 1, then
MCQ+3 / -12021
10Limits Continuity And Differentiability
The value of \(\mathop {\lim }\limits_{x \to 0} {{\sqrt {1 - {{\cos x}^2}} } \over {1 - \cos x}}\) is
MCQ+3 / -12021