AP EAMCET · Maths · Limits
Which one of the following function is discontinuous at \(\mathrm{x}=1 ?\)
- A \(f(x)=\sin ^2 x+\tan ^2 x+\cos ^2 x-\sec ^2 x\)
- B \(f(x)=\frac{1}{1+2^{\sin x}}\)
- C \(f(x)= \begin{cases}\frac{x-1}{|x-1|+2(x-1)^2}, & x \neq 1 \\ 1, & x=1\end{cases}\)
- D \(f(x)=e^x+5\)
Answer & Solution
Correct Answer
(C) \(f(x)= \begin{cases}\frac{x-1}{|x-1|+2(x-1)^2}, & x \neq 1 \\ 1, & x=1\end{cases}\)
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{cc}\frac{x-1}{|x-1|+2(x-1)^2} & x \neq 1 \\ 1 & x=1\end{array}\right.\) \(\Rightarrow f(x)=\left\{\begin{array}{cc}\frac{1}{2 x-1} & x>1 \\ \frac{1}{2 x-3} & x < 1 \\ 1 & x=1\end{array}\right.\)…
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