JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(f(x)=\left\{\begin{array}{ll}{\frac{\sin (a+2) x+\sin x}{x}} & {; x<0} \\ {b} & {; x=0} \\ {\frac{\left(x+3 x^{2}\right)^{\frac{1}{3}}-x^{\frac{1}{3}}}{x^{\frac{4}{3}}}} & {; x>0}\end{array}\right.\) is continuous at \(x=0,\) then \(a+2 b\) is equal to
- A \(-1\)
- B \(1\)
- C \(-2\)
- D \(0\)
Answer & Solution
Correct Answer
(D) \(0\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0}\left(\frac{\sin (a+2) x}{x}+\frac{\sin x}{x}\right)=a+3\) \(\lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0} \frac{\left(x+3 x^{2}\right)^{1 / 3}-x^{1 / 3}}{x^{4 / 3}}\)…
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