New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Limits Continuity and Differentiability question

2021 · 16 Mar · Shift 1 · Q24

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

PYQ Library
JEE Main
Mathematics
Limits Continuity and Differentiability
2021 · 16 Mar · Shift 1 · Q24

Limits Continuity and Differentiability question

2021 · 16 Mar · Shift 1 · Q24

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let

{S_k} = \sum\limits_{r = 1}^k {{{\tan }^{ - 1}}\left( {{{{6^r}} \over {{2^{2r + 1}} + {3^{2r + 1}}}}} \right)}

. Then

\mathop {\lim }\limits_{k \to \infty } {S_k}

is equal to :

A
${\cot ^{ - 1}}\left( {{3 \over 2}} \right)$
B
${\pi \over 2}$
C
tan $-$ 1 (3)
D
${\tan ^{ - 1}}\left( {{3 \over 2}} \right)$

More from Limits Continuity and Differentiability

Let the functions f : R $\to$ R and g : R $\to$ R be defined as : $f (x) = {x + 2, x^{2}, x < 0 x \geq 0$ and $g (x) = {x^{3}, 3 x - 2, x < 1 x \geq 1$ …2021 · MCQ
If $x \to 0 lim \frac{a e ^{x} - b c o s x + c e ^{- x}}{x s i n x} = 2$ , then a + b + c is equal to .2021 · Numerical
Let f : S $\to$ S where S = (0, $\infty$ ) be a twice differentiable function such that f(x + 1) = xf(x). If g : S $\to$ R be defined as g(x) = loge f(x), then the value of |g''(5) $-$ g''(1)| is equal to :2021 · MCQ
Let $α \in$ R be such that the function $f (x) = {\frac{c o s ^{- 1} ( 1 - { x } ^{2} ) s i n ^{- 1} ( 1 - { x })}{{ x } - { x } ^{3}}, α, x e 0 x = 0$ …2021 · MCQ
Let f : R $\to$ R and g : R $\to$ R be defined as $f (x) = {x + a, ∣ x - 1∣, x < 0 x \geq 0$ and $g (x) = {x + 1, (x - 1)^{2} + b, x < 0 x \geq 0$ …2021 · Numerical
The value of $x \to 0^{+} lim \frac{c o s ^{- 1} ( x - [ x ] ^{2} ) . s i n ^{- 1} ( x - [ x ] ^{2} )}{x - x ^{3}}$ , where [ x ] denotes the greatest integer $\leq$ x is :2021 · MCQ
If the function $f (x) = \frac{c o s ( s i n x ) - c o s x}{x ^{4}}$ is continuous at each point in its domain and $f (0) = \frac{1}{k}$ , then k is .2021 · Numerical
The value of the limit $θ \to 0 lim \frac{t a n ( π c o s ^{2} θ )}{s i n ( 2 π s i n ^{2} θ )}$ is equal to :2021 · MCQ