New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Limits Continuity and Differentiability question

2025 · 29 Jan · Shift 1 · Q35

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

PYQ Library
JEE Main
Mathematics
Limits Continuity and Differentiability
2025 · 29 Jan · Shift 1 · Q35

Limits Continuity and Differentiability question

2025 · 29 Jan · Shift 1 · Q35

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

The value of

\lim \limits_{n \rightarrow \infty}\left(\sum\limits_{k=1}^n \frac{k^3+6 k^2+11 k+5}{(k+3)!}\right)

is :

A
5/3
B
2
C
4/3
D
7/3

More from Limits Continuity and Differentiability

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
Let $f (x) = {x - 1, x is even, 2 x, x is odd, x \in N$ . If for some $a \in N, f (f (f (a))) = 21$ , then $x \to a^{-} lim {\frac{∣ x ∣ ^{3}}{a} - [\frac{x}{a}]}$ …2024 · MCQ
Let $f : R \to R$ be a function given by $f (x) = {\frac{1 - c o s 2 x}{x ^{2}}, x 0$ where $α, β \in R$ . If $f$ is continuous at $x = 0$ , then $α^{2} + β^{2}$ is equal…2024 · MCQ
If $lim_{x \to 1} \frac{( 5 x + 1 ) ^{1/3} - ( x + 5 ) ^{1/3}}{( 2 x + 3 ) ^{1/2} - ( x + 4 ) ^{1/2}} = \frac{m 5}{n ( 2 n ) ^{2/3}}$ , where $gcd (m, n) = 1$ , then $8 m + 12 n$ …2024 · Numerical