New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Limits Continuity and Differentiability question

2025 · 24 Jan · Shift 2 · Q42

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Limits Continuity and Differentiability
2025 · 24 Jan · Shift 2 · Q42

Limits Continuity and Differentiability question

2025 · 24 Jan · Shift 2 · Q42

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let

[x]

denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function

f(x)=[x]+|x-2|,-2\lt x\lt 3

, is not continuous and not differentiable. Then

\mathrm{m}+\mathrm{n}

is equal to :

A
6
B
9
C
8
D
7

More from Limits Continuity and Differentiability

Let $f (x) = {3 x, x 2$ where [.] denotes greatest integer function. If $α$ and $β$ are the number of points, where $f$ is not continuous and is not differentiable, respectively,…2025 · Numerical
Let $f (x) = n \to \infty lim r = 0 \sum n (\frac{t a n ( x / 2 ^{r + 1} ) + t a n ^{3} ( x / 2 ^{r + 1} )}{1 - t a n ^{2} ( x / 2 ^{r + 1} )})$ Then $x \to 0 lim \frac{e ^{x} - e ^{f (x)}}{( x - f ( x ))}$ …2025 · Numerical
The value of $n \to \infty lim (k = 1 \sum n \frac{k ^{3} + 6 k ^{2} + 11 k + 5}{( k + 3 )!})$ is :2025 · MCQ
Let [t] be the greatest integer less than or equal to t. Then the least value of p ∈ N for which $x \to 0^{+} lim (x ([\frac{1}{x}] + [\frac{2}{x}] + \dots + [\frac{p}{x}]) - x^{2} ([\frac{1}{x ^{2}}] + [\frac{2 ^{2}}{x ^{2}}] + \dots + [\frac{9 ^{2}}{x ^{2}}]) \geq 1$ …2025 · Numerical
Let the function $f (x) = (x^{2} - 1) x^{2} - a x + 2 + cos ∣ x ∣$ be not differentiable at the two points $x = α = 2$ and $x = β$ . Then the distance of the point $12 x + 5 y + 10 = 0$ from the line $12 x + 5 y + 10 = 0$ is equal to :2025 · MCQ
Let $f : R \to R$ be defined as : $f (x) = {\frac{a - b c o s 2 x}{x ^{2}}; x 1$ If $f$ is continuous everywhere in $R$ and $m$ is the number of points where $f$ is NOT differential…2024 · MCQ
Let ${x}$ denote the fractional part of $x$ and $f (x) = \frac{c o s ^{- 1} ( 1 - { x } ^{2} ) s i n ^{- 1} ( 1 - { x })}{{ x } - { x } ^{3}}, x e q 0$ . If $L$ and $R$ respectively denotes the left hand limit and the right hand limit…2024 · Numerical
Let $f (x) = 2 x^{2} + 5 x ∣ - 3∣, x \in R$ . If $m$ and $n$ denote the number of points where $f$ is not continuous and not differentiable respectively, then $m + n$ is equal to :2024 · MCQ