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  • Please solve RD Sharma class 12 chapter 8 Continuity exercise Fill in the blanks question 9 maths textbook solution

Please solve RD Sharma class 12 chapter 8 Continuity exercise Fill in the blanks question 9 maths textbook solution

Answers (1)

Answer: k=0
 

Hint:Use the formula of (a^{2}-b^{2})
 

Given:
f(x)=\left\{\begin{array}{l} \frac{x^{2}-9}{x-3}, x \neq 3 \\ 2 x+k, x=3 \end{array}\right.  is continuous at x=3

Solution:

               If f(x) is continuous at x=3 , then

                \begin{aligned} &\lim _{x \rightarrow 3} f(x)=f(3) \\ &\lim _{x \rightarrow 3} \frac{x^{2}-9}{x-3}=2(3)+k \end{aligned}

                \begin{aligned} &\lim _{x \rightarrow 3} \frac{(x-3)(x+3)}{x-3}=2(3)+k \\ &\lim _{x \rightarrow 3} x+3=6+k \end{aligned}

                \begin{aligned} &3+3=6+k \\ &6=6+k \\ &k=0 \; \; \; \; \; \; \; \; \; \; \; \; \; \quad\left[\because\left(a^{2}-b^{2}\right)=(a+b)(a-b)\right] \end{aligned}

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