New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Limits Continuity and Differentiability question

2021 · 26 Aug · Shift 1 · Q42

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

PYQ Library
JEE Main
Mathematics
Limits Continuity and Differentiability
2021 · 26 Aug · Shift 1 · Q42

Limits Continuity and Differentiability question

2021 · 26 Aug · Shift 1 · Q42

JEE MainMathematicsLimits Continuity and DifferentiabilityNumerical+4 / −1

Let a, b

\in

R, b

\in

0, Define a function

f(x) = \left\{ {\begin{matrix} {a\sin {\pi \over 2}(x - 1),} & {for\,x \le 0} \\ {{{\tan 2x - \sin 2x} \over {b{x^3}}},} & {for\,x \gt 0} \\ \end{matrix} } \right.

. If f is continuous at x = 0, then 10

-

ab is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Limits Continuity and Differentiability

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
The value of $h \to 0 lim 2 {\frac{3 s i n ( \frac{π}{6} + h ) - c o s ( \frac{π}{6} + h )}{3 h ( 3 c o s h - s i n h )}}$ is :2021 · MCQ
Let f(x) be a differentiable function at x = a with f'(a) = 2 and f(a) = 4. Then $x \to a lim \frac{x f ( a ) - a f ( x )}{x - a}$ equals :2021 · MCQ
Let $f (x) = sin^{- 1} x$ and $g (x) = \frac{x ^{2} - x - 2}{2 x ^{2} - x - 6}$ . If $g (2) = x \to 2 lim g (x)$ , then the domain of the function fog is :2021 · MCQ
Let $f : R \to R$ be defined as $f (x) = ⎩ ⎨ ⎧ 2 sin (- \frac{π x}{2}) ∣ a x^{2} + x + b ∣ sin (π x) if x < - 1 if - 1 \leq x \leq 1 if x > 1$ …2021 · MCQ
If $α$ , $β$ are the distinct roots of x2 + bx + c = 0, then $x \to β lim \frac{e ^{2 (x^{2} + b x + c)} - 1 - 2 ( x ^{2} + b x + c )}{( x - β ) ^{2}}$ is equal to :2021 · MCQ
If $x \to \infty lim (x^{2} - x + 1 - a x) = b$ , then the ordered pair (a, b) is :2021 · MCQ