The function $f$ defined by $f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{{\sin {x^2}}}{x},x \ne 0}\\ {0,x = 0} \end{array}} \right.$ is

Neither continuous nor derivable at $x = 0$

Continuous but not derivable at $x = 0$

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Analyzing +4 | -1

The function

f

defined by

f\left( x \right) = \left\{ {\begin{array}{cccccccccccccccccccc} {\frac{{\sin {x^2}}}{x},x \ne 0}\\ {0,x = 0} \end{array}} \right.

View answer and explanation

Correct option: A

Continuous and derivable at

x = 0

Option A (Continuous and derivable at

x = 0

) is correct because the function is both continuous and differentiable at the specified point.

Practice All Chapter MCQs →

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

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x

y

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x y=1

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[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}}