Let a, b R, (a ≠ 0). If the function f defined as f(x) = \ (2x²)/a, 0 ≤ x < 1 a, 1 ≤ x < 2 (2b² - 4b)/(x³), 2 ≤ x < ∞. is continuous in the interval [0, ∞), then an ordered pair (a, b) is:

Limit, Continuity and Differentiability: JEE Main 2016 Mathematics question

JEE Main 2016 · 10 Apr, Morning shift · Q4129

JEE Main 201610 Apr, Morning shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002

Let a, b

\in

R, (a

\ne

0). If the function f defined as

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

is continuous in the interval [0,

\infty

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