Let f : R … R be defined as … If f is continuous at x = 0, then … is equal to :

Limits Continuity and Differentiability

JEE Main 2021 · 22 Jul, Evening shift · Q4147

MathematicsMedium179×since 2002Q4147

Let f : R

\to

R be defined as

f(x) = \left\{ {\matrix{ {{{{x^3}} \over {{{(1 - \cos 2x)}^2}}}{{\log }_e}\left( {{{1 + 2x{e^{ - 2x}}} \over {{{(1 - x{e^{ - x}})}^2}}}} \right),} & {x \ne 0} \cr {\alpha ,} & {x = 0} \cr } } \right.

If f is continuous at x = 0, then

\alpha

is equal to :

JEE Main 2021 · 22 Jul, Evening shift · Q4147

MathematicsMedium179×since 2002Q4147

Let f : R

\to

R be defined as

f(x) = \left\{ {\matrix{ {{{{x^3}} \over {{{(1 - \cos 2x)}^2}}}{{\log }_e}\left( {{{1 + 2x{e^{ - 2x}}} \over {{{(1 - x{e^{ - x}})}^2}}}} \right),} & {x \ne 0} \cr {\alpha ,} & {x = 0} \cr } } \right.

If f is continuous at x = 0, then

\alpha

is equal to :