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  • explain solution RD Sharma class 12 chapter 8 Continuity exercise Very short answer question 12 maths

explain solution RD Sharma class 12 chapter 8 Continuity exercise Very short answer question 12 maths

Answers (1)

Answer: 7

Hint: \lim _{x \rightarrow 2} f(x)=f(2)

Given: f(x)=\left\{\begin{array}{l} \frac{x^{2}+3 x-10}{x-2}, x \neq 2 \\ k, x=2 \end{array}\right. is continuous at x = 2

Explanation:

                As f(x) is continuous at x = 2 and

                \begin{aligned} &\lim _{x \rightarrow 2} f(x)=f(2) \\ &\lim _{x \rightarrow 2} \frac{x^{2}+3 x-10}{x-2}=k \\ &\lim _{x \rightarrow 2} \frac{x^{2}+5 x-2 x-10}{x-2}=k \\ &\lim _{x \rightarrow 2} \frac{(x-2)(x+5)}{x-2}=k \\ &\lim _{x \rightarrow 2} x+5=k \\ &\therefore k=7 \end{aligned}

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