AP EAMCET · Maths · Limits
If \(f(x)=\left\{\begin{array}{cl}1+\frac{2 x}{a}, & 0 \leq x \leq 1 \\ a x, & 1 \lt x \leq 2\end{array}\right.\). If \(\lim _{x \rightarrow 1} f(x)\) exists then the sum of the cubes of the possible values of \(a\) is
- A 1
- B 5
- C 7
- D 9
Answer & Solution
Correct Answer
(C) 7
Step-by-step Solution
Detailed explanation
\(\because \lim _{x \rightarrow 1} f(x)\) exists \(\Rightarrow \lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1^{+}} f(x)\) \(\Rightarrow 1+\frac{2}{a}=a \Rightarrow a^2-a-2=0 \Rightarrow a=-1,2\) Sum of the cubes \(=(-1)^3+(2)^3=-1+8=7\).
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