New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Limits Continuity and Differentiability question

2021 · 25 Feb · Shift 1 · Q32

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

PYQ Library
JEE Main
Mathematics
Limits Continuity and Differentiability
2021 · 25 Feb · Shift 1 · Q32

Limits Continuity and Differentiability question

2021 · 25 Feb · Shift 1 · Q32

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

\mathop {\lim }\limits_{n \to \infty } {\left( {1 + {{1 + {1 \over 2} + ........ + {1 \over n}} \over {{n^2}}}} \right)^n}

is equal to :

A
${{1 \over 2}}$
B
1
C
0
D
${{1 \over e}}$

More from Limits Continuity and Differentiability

The number of points, at which the function f(x) = | 2x + 1 | $-$ 3| x + 2 | + | x2 + x $-$ 2 |, x $\in$ R is not differentiable, is .2021 · Numerical
A function f is defined on [ $-$ 3, 3] as $f (x) = {min {∣ x ∣, 2 - x^{2}}, [∣ x ∣], - 2 \leq x \leq 2 2 < ∣ x ∣ \leq 3$ where [x] denotes the greatest integer $\leq$ x.…2021 · Numerical
If $x \to 0 lim \frac{a x - ( e ^{4 x} - 1 )}{a x ( e ^{4 x} - 1 )}$ exists and is equal to b, then the value of a $-$ 2b is .2021 · Numerical
Let f : R $\to$ R be defined as $f (x) = ⎩ ⎨ ⎧ \frac{λ ∣ x ^{2} - 5 x + 6 ∣}{μ ( 5 x - x ^{2} - 6 )}, e^{\frac{t a n ( x - 2 )}{x - [ x ]}}, μ, x < 2 x > 2 x = 2$ …2021 · MCQ
Consider the function where P(x) is a polynomial such that P'' (x) is always a constant and P(3) = 9. If f(x) is continuous at x = 2, then P(5) is equal to . Includes diagram2021 · Numerical
Let a, b $\in$ R, b $\in$ 0, Define a function $f (x) = {a sin \frac{π}{2} (x - 1), \frac{t a n 2 x - s i n 2 x}{b x ^{3}}, f or x \leq 0 f or x > 0$ . If f is…2021 · Numerical
Let [t] denote the greatest integer less than or equal to t. Let f(x) = x $-$ [x], g(x) = 1 $-$ x + [x], and h(x) = min{f(x), g(x)}, x $\in$ [ $-$ 2, 2]. Then h is :2021 · MCQ
$x \to 2 lim (n = 1 \sum 9 \frac{x}{n ( n + 1 ) x ^{2} + 2 ( 2 n + 1 ) x + 4})$ is equal to :2021 · MCQ