JEE MATHEMATICS MCQ: DIFFERENTIATION

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Analyzing +4 | -1

Let

f: R \rightarrow R

be a twice differentiable function such that

\lim \limits_{{x \rightarrow \infty}} f(x)=a(a \neq 0)

, then

\lim \limits_{{x \rightarrow \infty}} x^2 f^{\prime \prime}(x)

is equal to

View answer and explanation

Correct option: D

None of these

Option B (

\frac{{1}}{{16}}

) is correct because it represents the maximum value obtained by completing the square and integrating.

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f(x)=|x|^{|\tan x|}

f^{\prime}\left(\frac{-\pi}{6}\right)

x

y

x>0

x y=1

x+y

f(x)=[x] \sin (\pi x)

[x]

x

x=k, k

f(x)

y = {\sec ^{ - 1}}\left[ {\mathrm{cosec}x} \right] + \mathrm{cose}{\mathrm{c}^{ - 1}}\left[ {\sec x} \right] + {\sin ^{ - 1}}[\cos x] + {\cos ^{ - 1}}[\sin x],

\frac{{dy}}{{dx}}

\frac{d}{d x} \sin ^{-1}\left(3 x-4 x^{3}\right)

z = y + f\left( v \right),

v = \left( {\frac{x}{y}} \right),

v\frac{{\partial z}}{{\partial x}} + \frac{{\partial z}}{{\partial y}}