New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Limits Continuity and Differentiability question

2002 · Shift 0 · Q68

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

PYQ Library
JEE Main
Mathematics
Limits Continuity and Differentiability
2002 · Shift 0 · Q68

Limits Continuity and Differentiability question

2002 · Shift 0 · Q68

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

\mathop {\lim }\limits_{x \to 0} {{\log {x^n} - \left[ x \right]} \over {\left[ x \right]}}

,

n \in N

, ( [x] denotes the greatest integer less than or equal to x )

A
has value $-1$
B
has value $0$
C
has value $1$
D
does not exist

More from Limits Continuity and Differentiability

If $f (1) = 1, f^{'} (1) = 2,$ then $x \to 1 lim \frac{f ( x ) - 1}{x - 1}$ is2002 · MCQ
$f$ is defined in $[- 5, 5]$ as $f (x) = x$ if $x$ is rational $= - x$ if $x$ is irrational. Then2002 · MCQ
If f(x + y) = f(x).f(y) $\forall$ x, y and f(5) = 2, f'(0) = 3, then f'(5) is2002 · MCQ
For $α, β, γ \in R$ , if $lim_{x \to 0} \frac{x ^{2} s i n α x + ( γ - 1 ) e ^{x^{2}}}{s i n 2 x - β x} = 3$ , then $β + γ - α$ is equal to :2025 · MCQ
$I f x \to 0 lim \frac{c o s ( 2 x ) + a c o s ( 4 x ) - b}{x ^{4}} i s f ini t e, t h e n (a + b) i s e q u a l t o :$ 2025 · MCQ
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