Mathematics · 2021
JEE Main · 18 March 2021, Shift 2 · Q72
Let f: R → R be a function defined as f(x)= {(sin ( a +1) x+ sin 2 x)/(2 x), if x<0; b, if x=0; (√(x+ b x^3)-√ x)/(b x^5 / 2), if x>0} If f is…
Let $\displaystyle f: \mathbf{R} \rightarrow \mathbf{R}$ be a function defined as
$$f(x)= \begin{cases}\frac{\sin (\mathrm{a}+1) x+\sin 2 x}{2 x} & , \text { if } x<0 \\ \mathrm{~b} & , \text { if } x=0 \\ \frac{\sqrt{x+\mathrm{b} x^3}-\sqrt{x}}{\mathrm{~b} x^{5 / 2}} & , \text { if } x>0\end{cases}
$$
If $\displaystyle f$ is continuous at $\displaystyle x=0$, then the value of $\displaystyle \mathrm{a}+\mathrm{b}$ is equal to :
Official answer
(4)
$\displaystyle -\frac{3}{2}$
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.