Let f: R → R be a function defined as f(x) = \ (sin (a + 1)x + sin 2x)/2x,if x 0. If f is continuous at x = 0, then the value of a + b is equal to:

Limit, Continuity and Differentiability: JEE Main 2021 Mathematics question

JEE Main 2021 · 18 Mar, Evening shift · Q4145

JEE Main 202118 Mar, Evening shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002

Let f : R

\to

R be a function defined as

f(x) = \left\{ \matrix{ {{\sin (a + 1)x + \sin 2x} \over {2x}},if\,x < 0 \hfill \cr b,\,if\,x\, = 0 \hfill \cr {{\sqrt {x + b{x^3}} - \sqrt x } \over {b{x^{5/2}}}},\,if\,x > 0 \hfill \cr} \right.

If f is continuous at x = 0, then the value of a + b is equal to :

JEE Main 2021 · 18 Mar, Evening shift · Q4145

JEE Main 202118 Mar, Evening shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002

Let f : R

\to

R be a function defined as

f(x) = \left\{ \matrix{ {{\sin (a + 1)x + \sin 2x} \over {2x}},if\,x < 0 \hfill \cr b,\,if\,x\, = 0 \hfill \cr {{\sqrt {x + b{x^3}} - \sqrt x } \over {b{x^{5/2}}}},\,if\,x > 0 \hfill \cr} \right.

If f is continuous at x = 0, then the value of a + b is equal to :