CUET · MATHS · PYQ PAPER 2023
The value of k for which the function \(f(x)=\left\{\begin{array}{ll}\frac{x^2+3 x-10}{x-2} & x \neq 2 \\ k & x=2\end{array}\right.\) is continuous at x = 2 is:
- A 3
- B 7
- C 2
- D 5
Answer & Solution
Correct Answer
(B) 7
Step-by-step Solution
Detailed explanation
For continuity at \(x=2\), \(\lim_{x \to 2} f(x) = f(2)\). \(f(2) = k\) \(\lim_{x \to 2} \frac{x^2+3x-10}{x-2} = \lim_{x \to 2} \frac{(x+5)(x-2)}{x-2}\) \(\lim_{x \to 2} (x+5) = 2+5 = 7\) \(k = 7\)
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