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Limits, continuity and differentiability Revision for JEE

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Revise Limits, continuity and differentiability by covering every subtopic once, drilling formulas, then solving 28+ timed MCQs with full solutions.

Use this Limits, continuity and differentiability revision checklist before mocks and the final exam. Reinforce concepts with 28+ syllabus-aligned MCQs on Goodmarks.

Revision checklist

  1. 1.Core idea: Limits, continuity and differentiability
  2. 2.Relates to other subtopics in Limit, Continuity and Differentiability
  3. 3.Limits and continuity
  4. 4.Chain rule, implicit, logarithmic differentiation
  5. 5.Master Limits, continuity and differentiability definitions and standard results
  6. 6.Solve 20 timed MCQs for Limits, continuity and differentiability

Syllabus context

Part of Limit, Continuity and Differentiability in JEE Main Mathematics.

Free sample questions

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Q1MathsUnit 7: Limit, Continuity and Differentiability
Let f(x)=x3−x2+x+1\boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1} and g(x)=\boldsymbol{g}(\boldsymbol{x})= {max⁡{f(t)},0≤t≤x0≤x≤13−x,1<x≤2\left\{\begin{array}{l}\max \{f(t)\}, \quad 0 \leq t \leq x \quad 0 \leq x \leq 1 \\ 3-x, \quad 1<x \leq 2\end{array}\right. Then in the interval [0,2],g(x)[0,2], g(x) is This question has multiple correct options
Q2MathsUnit 7: Limit, Continuity and Differentiability
A polynomial p(x)p(x) when divided by x2−x^{2}- 3x+23 x+2 leaves remainder 2x−3.2 x-3 . Then
Q3MathsUnit 7: Limit, Continuity and Differentiability
\operatorname{Let} f(x)=\left\{\begin{array}{cc}-1, & -2 \leq x<0 \\ x^{2}-1, & 0<x \leq 2\end{array} and \right. g(x)=∣f(x)∣+f∣x∣\boldsymbol{g}(\boldsymbol{x})=|\boldsymbol{f}(\boldsymbol{x})|+\boldsymbol{f}|\boldsymbol{x}| then the number of points which g(x)g(x) is non differentiable, is
Q4MathsUnit 7: Limit, Continuity and Differentiability
Arrange the following limits in the ascending order: (1) lim⁡x→∞(1+x2+x)x+2\lim _{x \rightarrow \infty}\left(\frac{1+x}{2+x}\right)^{x+2} (2) lim⁡x→0(1+2x)3/x\lim _{x \rightarrow 0}(1+2 x)^{3 / x} (3) lim⁡θ→0sin⁡θ2θ\lim _{\boldsymbol{\theta} \rightarrow \mathbf{0}} \frac{\sin \boldsymbol{\theta}}{\mathbf{2} \boldsymbol{\theta}} (4) lim⁡x→0log⁡e(1+x)x\lim _{x \rightarrow 0} \frac{\log _{e}(1+x)}{x}
Q5MathsUnit 7: Limit, Continuity and Differentiability
Assertion lim⁡x→01−cos⁡2xx\lim _{\boldsymbol{x} \rightarrow \mathbf{0}} \frac{\sqrt{1-\cos 2 x}}{\boldsymbol{x}} does not exist. Reason ∣sin⁡x∣={sin⁡x;0<x<π2−sin⁡x;−π2<x<0|\sin x|=\left\{\begin{array}{cc}\sin x ; & 0<x<\frac{\pi}{2} \\ -\sin x ; & -\frac{\pi}{2}<x<0\end{array}\right.
Q6MathsUnit 7: Limit, Continuity and Differentiability
Let f(x)\boldsymbol{f}(\boldsymbol{x}) be defined in the interval [-2,2] such that f(x)=f(x)= {−1,−2≤x≤0x−1,0<x≤2 and g(x)=\left\{\begin{array}{ll}-1, & -2 \leq x \leq 0 \\ x-1, & 0<x \leq 2\end{array} \text { and } g(x)=\right. f(∣x∣)+∣f(x)∣\boldsymbol{f}(|\boldsymbol{x}|)+|\boldsymbol{f}(\boldsymbol{x})| Test the differentiablity of g(x)g(x) in (-2,2)
Q7MathsUnit 7: Limit, Continuity and Differentiability
The function f(x)=f(x)= \left\{\begin{array}{l}\frac{\cos 3 x-\cos 4 x}{x^{2}}, \text { for } x \neq 0 \\ \frac{7}{2}, \text { for } x=0\end{array} at \right. x=0\boldsymbol{x}=\mathbf{0} is
Q8MathsUnit 7: Limit, Continuity and Differentiability
Assertion If f(x)=0f(x)=0 has two distinct positive real roots then number of non- differentiable points of y=∣f(−∣x∣)∣\boldsymbol{y}=|\boldsymbol{f}(-|\boldsymbol{x}|)| is 1\mathbf{1} Reason Graph of y=f(∣x∣)\boldsymbol{y}=\boldsymbol{f}(|\boldsymbol{x}|) is symmetrical about y-axis

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Follow the checklist on this page, revise formulas daily, and attempt mixed MCQs every 2–3 days.

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