JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If the function \(f\) defined as \(f(x)\, = \frac{1}{x} - \frac{{k - 1}}{{{e^{2x}} - 1}}\) ,\(x\, \ne \,0,\) is continuous at \(x = 0.\) then the ordered pair \((k,f(0))\) is equal to?
- A \((3, 1 )\)
- B \((3, 2)\)
- C \(\left( {\frac{1}{3},2} \right)\)
- D \((2, 1)\)
Answer & Solution
Correct Answer
(A) \((3, 1 )\)
Step-by-step Solution
Detailed explanation
if the funtion is continuous at \(x=0\), then \(\mathop {\lim }\limits_{x \to 0} f\left( x \right)\) will exist and \(f\left( 0 \right) = \mathop {\lim }\limits_{x \to 0} f\left( x \right)\) Now,…
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