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Limits Continuity and Differentiability question

2016 · 10 Apr · Shift 1 · Q41

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JEE Main
Mathematics
Limits Continuity and Differentiability
2016 · 10 Apr · Shift 1 · Q41

Limits Continuity and Differentiability question

2016 · 10 Apr · Shift 1 · Q41

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let a, b

\in

R, (a

e

0). If the function f defined as

f\left( x \right) = \left\{ {\begin{matrix} {{{2{x^2}} \over a}\,\,,} & {0 \le x \lt 1} \\ {a\,\,\,,} & {1 \le x \lt \sqrt 2 } \\ {{{2{b^2} - 4b} \over {{x^3}}},} & {\sqrt 2 \le x \lt \infty } \\ \end{matrix} } \right.

is continuous in the interval [0,

\infty

), then an ordered pair ( a, b) is :

A
$\left( {\sqrt 2 ,1 - \sqrt 3 } \right)$
B
$\left( { - \sqrt 2 ,1 + \sqrt 3 } \right)$
C
$\left( {\sqrt 2 , - 1 + \sqrt 3 } \right)$
D
$\left( { - \sqrt 2 ,1 - \sqrt 3 } \right)$

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