JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f: R \rightarrow R\) be a function defined as \(f(x)=\left\{\begin{array}{cl}\frac{\sin (a+1) x+\sin 2 x}{2 x} & , \text { if } x<0 \\ b & , \text { if } x=0 \\ \frac{\sqrt{x+b x^{3}}-\sqrt{x}}{b x^{5 / 2}} & , \text { if } x>0\end{array}\right.\) . If \(f\) is continuous at \(x=0,\) then the value of \(a + b\) is equal to ....... .
- A \(-\frac{5}{2}\)
- B \(-2\)
- C \(-3\)
- D \(-\frac{3}{2}\)
Answer & Solution
Correct Answer
(D) \(-\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
\(f(x)\) is continuous at \(x=0\) \(\lim _{x \rightarrow 0^{+}} f(x)=f(0)=\lim _{x \rightarrow 0^{-}} f(x)....(1)\) \(f(0)= b....(2)\) \(\lim _{x \rightarrow 0^{+}} f(x)=\lim _{x \rightarrow 0^{+}}\left(\frac{\sin (a+1) x}{2 x}+\frac{\sin 2 x}{2 x}\right)\)…
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