New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Limits Continuity and Differentiability question

2025 · 2 Apr · Shift 2 · Q32

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

PYQ Library
JEE Main
Mathematics
Limits Continuity and Differentiability
2025 · 2 Apr · Shift 2 · Q32

Limits Continuity and Differentiability question

2025 · 2 Apr · Shift 2 · Q32

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

If\,\mathop {\lim }\limits_{x \to 0} {{\cos (2x) + a\cos (4x) - b} \over {{x^4}}}is\,finite,\,then\,(a + b)\,is\,equal\,to:

A
0
B
$\frac{3}{4}$
C
-1
D
$\frac{1}{2}$

More from Limits Continuity and Differentiability

Let $f (x) = {(1 + a x)^{1/ x}, x 0$ be continuous at $x = 0$ . Then $e^{a} b c$ is equal to:2025 · MCQ
If $x \to 0 lim (\frac{t a n x}{x})^{\frac{1}{x ^{2}}} = p$ , then $96 lo g_{e} p$ is equal to 2025 · Numerical
Let $f : R \to R$ be a continuous function satisfying $f (0) = 1$ and $f (2 x) - f (x) = x$ for all $x \in R$ . If $lim_{n \to \infty} {f (x) - f (\frac{x}{2 ^{n}})} = G (x)$ , then $\sum_{r = 1}^{10} G (r^{2})$ …2025 · MCQ
If $lim_{x \to 1^{+}} \frac{( x - 1 ) ( 6 + λ c o s ( x - 1 )) + μ s i n ( 1 - x )}{( x - 1 ) ^{3}} = - 1$ , where $λ, μ \in R$ , then $λ + μ$ is equal to2025 · MCQ
Let $m$ and $n$ be the number of points at which the function $f (x) = max {x, x^{3}, x^{5}, \dots x^{21}}, x \in R$ , is not differentiable and not continuous, respectively. Then $m + n$ is equal to…2025 · Numerical
Let $f$ be a differentiable function on $R$ such that $f (2) = 1, f^{'} (2) = 4$ . Let $x \to 0 lim (f (2 + x))^{3/ x} = e^{α}$ . Then the number of times the curve $y = 4 x^{3} - 4 x^{2} - 4 (α - 7) x - α$ meets…2025 · MCQ
$lim_{x \to 0^{+}} \frac{t a n ( 5 ( x ) ^{\frac{1}{3}} ) l o g _{e} ( 1 + 3 x ^{2} )}{( t a n ^{- 1} 3 x ) ^{2} ( e ^{5 (x)^{\frac{4}{3}}} - 1 )}$ is equal to2025 · MCQ
The number of points of discontinuity of the function $f (x) = [\frac{x ^{2}}{2}] - [x], x \in [0, 4]$ , where $[\cdot]$ denotes the greatest integer function, is .2025 · Numerical