AP EAMCET · Maths · Continuity and Differentiability
If a function \(f(x)=\left\{\begin{array}{cc}\frac{\tan (\alpha+1) x+\tan 2 x}{x} & \text { if } x\gt0 \\ \beta & \text { at } x=0 \\ \frac{\sin 3 x-\tan 3 x}{x^3} & \text { if } x \lt 0\end{array}\right.\)
is continuous at \(x=0\) then \(|\alpha|+|\beta|=\)
- A \(60\)
- B \(30\)
- C \(15\)
- D \(45\)
Answer & Solution
Correct Answer
(B) \(30\)
Step-by-step Solution
Detailed explanation
\(f^{\prime}(x)\) is continuous at \(x=0\) \(\lim _{x \rightarrow 0^{+}} f(x)=f(0)=\beta\) \(\lim _{x \rightarrow 0^{+}} \frac{\tan (\alpha+1) x+\tan 2 x}{x}=\alpha+3=\beta \Rightarrow \lim _{x \rightarrow 0^{-}} f(x)=\beta\)…
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