Let f: R → R be defined as f(x) = \ x⁵ sin (1/x) + 5x², x 0. The value of λ for which f ''(0) exists, is _ _ _ _.

Limit, Continuity and Differentiability: JEE Main 2020 Mathematics question

JEE Main 2020 · 6 Sep, Morning shift · Q32

JEE Main 20206 Sep, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let f : R

\to

R be defined as

f\left( x \right) = \left\{ {\matrix{ {{x^5}\sin \left( {{1 \over x}} \right) + 5{x^2},} & {x < 0} \cr {0,} & {x = 0} \cr {{x^5}\cos \left( {{1 \over x}} \right) + \lambda {x^2},} & {x > 0} \cr } } \right.

The value of

\lambda

for which f ''(0) exists, is _______.

Your answerType your answer. Integers and decimals are accepted.