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  • provide solution for RD Sharma maths class 12 chapter 8 Continuity exercise Fill in the blanks question 10

provide solution for RD Sharma maths class 12 chapter 8 Continuity exercise  Fill in the blanks question 10

Answers (1)

Answer: 2

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

Given:f(x)=\left\{\begin{array}{cl} \frac{x^{2}-1}{x-1}, & x \neq 1 \\ k & , x=1 \end{array} \text { is continuous at } x=1\right.

Solution:

               If f(x) is continuous at x=1, then

                \begin{aligned} &\lim _{x \rightarrow 1} f(x)=f(1) \\ &\lim _{x \rightarrow 1} \frac{x^{2}-1}{x-1}=k \end{aligned}

                \lim _{x \rightarrow 1} \frac{(x-1)(x+1)}{x-1}=k \; \; \; \; \; \; \; \; \quad\left[\because\left(a^{2}-b^{2}\right)=(a+b)(a-b)\right]

                \begin{aligned} &\lim _{x \rightarrow 1} x+1=k \\ &1+1=k \\ &k=2 \end{aligned}

                

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