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Question
Find the value of k for which the function f (x ) = \[\binom{\frac{x^2 + 3x - 10}{x - 2}, x \neq 2}{ k , x^2 }\] is continuous at x = 2 .
Solution
Given,
f (x ) = \[\binom{\frac{x^2 + 3x - 10}{x - 2}, x \neq 2}{ k , x=2 }\]
\[\lim_{x \to 2^-} \left( \frac{x^2 + 3x - 10}{x - 2} \right) = \lim_{x \to 2^-} \left( x + 5 \right) = 7\]
\[f\left( 2 \right) = k\]
\[ \lim_{x \to 2^+} \left( \frac{x^2 + 3x - 10}{x - 2} \right) = \lim_{x \to 2^+} \left( x + 5 \right) = 7\]
If f ( x) is continuous at x = 2 , then
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