New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Limits Continuity and Differentiability question

2022 · 29 Jul · Shift 1 · Q29

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

PYQ Library
JEE Main
Mathematics
Limits Continuity and Differentiability
2022 · 29 Jul · Shift 1 · Q29

Limits Continuity and Differentiability question

2022 · 29 Jul · Shift 1 · Q29

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

If

\lim\limits_{x \rightarrow 0} \frac{\alpha \mathrm{e}^{x}+\beta \mathrm{e}^{-x}+\gamma \sin x}{x \sin ^{2} x}=\frac{2}{3}

, where

\alpha, \beta, \gamma \in \mathbf{R}

, then which of the following is NOT correct?

A
$\alpha^{2}+\beta^{2}+\gamma^{2}=6$
B
$\alpha \beta+\beta \gamma+\gamma \alpha+1=0$
C
$\alpha\beta^{2}+\beta \gamma^{2}+\gamma \alpha^{2}+3=0$
D
$\alpha^{2}-\beta^{2}+\gamma^{2}=4$

More from Limits Continuity and Differentiability

The number of points, where the function $f : R \to R$ , $f (x) = ∣ x - 1∣ cos ∣ x - 2∣ sin ∣ x - 1∣ + (x - 3) x^{2} - 5 x + 4$ , is NOT differentiable, is :2022 · MCQ
$Let the function f (x) = {\frac{l o g _{e} ( 1 + 5 x ) - l o g _{e} ( 1 + α x )}{x} 10; if x e q 0; if x = 0 be continuous at x = 0.$ Then $α$ is…2022 · MCQ
If $[t]$ denotes the greatest integer $\leq t$ , then the number of points, at which the function $f (x) = 4∣2 x + 3∣ + 9 [x + \frac{1}{2}] - 12 [x + 20]$ is not differentiable in the open interval $(- 20, 20)$ , is .2022 · Numerical
The value of $x \to 1 lim \frac{( x ^{2} - 1 ) s i n ^{2} ( π x )}{x ^{4} - 2 x ^{3} + 2 x - 1}$ is equal to:2022 · MCQ
Suppose $x \to 0 lim \frac{F ( x )}{x ^{3}}$ exists and is equal to L, where $F (x) = a + sin \frac{x}{2} - b cos x 0 - b cos x 0 a + sin \frac{x}{2} 0 a + sin \frac{x}{2} - b cos x$ …2022 · Numerical
Let $f (x) = x^{6} + 2 x^{4} + x^{3} + 2 x + 3$ , x $\in$ R. Then the natural number n for which $x \to 1 lim \frac{x ^{n} f ( 1 ) - f ( x )}{x - 1} = 44$ is .2021 · Numerical
Let [t] denote the greatest integer $\leq$ t. The number of points where the function $f (x) = [x] x^{2} - 1 + sin (\frac{π}{[ x ] + 3}) - [x + 1], x \in (- 2, 2)$ is not continuous is …2021 · Numerical
Let $S_{k} = r = 1 \sum k tan^{- 1} (\frac{6 ^{r}}{2 ^{2 r + 1} + 3 ^{2 r + 1}})$ . Then $k \to \infty lim S_{k}$ is equal to :2021 · MCQ