COMEDK · Maths · 25. Continuity and Differentiability
If \(f(x) = \begin{cases} \dfrac{\sqrt{1+x} - \sqrt{1-x}}{\sin x}, & x \neq 0 \\ k, & x = 0 \end{cases}\) is continuous at \(x = 0\), then \(k =\)
- A \(2\)
- B \(\dfrac{1}{2}\)
- C \(1\)
- D \(0\)
Answer & Solution
Correct Answer
(C) \(1\)
Step-by-step Solution
Detailed explanation
For the function to be continuous at \(x = 0\), we must have \(\lim_{x \to 0} f(x) = f(0) = k\). \(\lim_{x \to 0} \dfrac{\sqrt{1+x} - \sqrt{1-x}}{\sin x}\) Rationalizing the numerator:…
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