If f(x) = \ (sin (a + 2)x + sin x)/x; x 0. is continuous at x = 0, then a + 2b is equal to:

Limit, Continuity and Differentiability: JEE Main 2020 Mathematics question

JEE Main 2020 · 9 Jan, Morning shift · Q4141

JEE Main 20209 Jan, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

f(x) = \left\{ {\matrix{ {{{\sin (a + 2)x + \sin x} \over x};} & {x < 0} \cr {b\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,;} & {x = 0} \cr {{{{{\left( {x + 3{x^2}} \right)}^{{1 \over 3}}} - {x^{ {1 \over 3}}}} \over {{x^{{4 \over 3}}}}};} & {x > 0} \cr } } \right.

is continuous at x = 0, then a + 2b is equal to :

JEE Main 2020 · 9 Jan, Morning shift · Q4141

JEE Main 20209 Jan, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

f(x) = \left\{ {\matrix{ {{{\sin (a + 2)x + \sin x} \over x};} & {x < 0} \cr {b\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,;} & {x = 0} \cr {{{{{\left( {x + 3{x^2}} \right)}^{{1 \over 3}}} - {x^{ {1 \over 3}}}} \over {{x^{{4 \over 3}}}}};} & {x > 0} \cr } } \right.

is continuous at x = 0, then a + 2b is equal to :