New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Limits Continuity and Differentiability question

2024 · 9 Apr · Shift 2 · Q45

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

PYQ Library
JEE Main
Mathematics
Limits Continuity and Differentiability
2024 · 9 Apr · Shift 2 · Q45

Limits Continuity and Differentiability question

2024 · 9 Apr · Shift 2 · Q45

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

\lim_{x \rightarrow 0} \frac{e-(1+2 x)^{\frac{1}{2 x}}}{x}

is equal to

A
$\frac{-2}{e}$
B
$e-e^2$
C
0
D
$e$

More from Limits Continuity and Differentiability

Consider the function. $f (x) = ⎩ ⎨ ⎧ \frac{a ( 7 x - 12 - x ^{2} )}{b ∣ x ^{2} - 7 x + 12 ∣} b, x 3, x = 3,$ where $[x]$ denotes the greatest integer less…2024 · MCQ
If $a = x \to 0 lim \frac{1 + 1 + x ^{4} - 2}{x ^{4}}$ and $b = x \to 0 lim \frac{s i n ^{2} x}{2 - 1 + c o s x}$ , then the value of $a b^{3}$ is :2024 · MCQ
Consider the function $f : (0, 2) \to R$ defined by $f (x) = \frac{x}{2} + \frac{2}{x}$ and the function $g (x)$ defined by $g (x) = {min ⌊ f (t)}, \frac{3}{2} + x, 0 < t \leq x and 0 < x \leq 1 1 < x < 2 . Then,$ …2024 · MCQ
$If lim_{x \to 0} \frac{3 + α s i n x + β c o s x + l o g _{e} ( 1 - x )}{3 t a n ^{2} x} = \frac{1}{3}, then 2 α - β is equal to :$ 2024 · MCQ
Let $f (x) = lim_{r \to x} {\frac{2 r ^{2} [ ( f ( r ) ) ^{2} - f ( x ) f ( r ) ]}{r ^{2} - x ^{2}} - r^{3} e^{\frac{f ( r )}{r}}}$ be differentiable in $(- \infty, 0) \cup (0, \infty)$ and $f (1) = 1$ . Then the value of ea, such that…2024 · Numerical
If the function $f (x) = {\frac{1}{∣ x ∣}, a x^{2} + 2 b, ∣ x ∣ ⩾ 2 ∣ x ∣ < 2$ is differentiable on $R$ , then $48 (a + b)$ is equal to .2024 · Numerical
$lim_{x \to 0} \frac{e ^{2∣ s i n x ∣} - 2∣ s i n x ∣ - 1}{x ^{2}}$ 2024 · MCQ
Let $g (x)$ be a linear function and $f (x) = {g (x) (\frac{1 + x}{2 + x})^{\frac{1}{x}}, x \leq 0, x > 0$ , is continuous at $x = 0$ . If $f^{'} (1) = f (- 1)$ , then the value $g (3)$ …2024 · MCQ