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  • Explain solution RD Sharma class 12 Chapter 8 Continuity exercise 8.1 question 18

Explain solution RD Sharma class 12 Chapter 8 Continuity exercise 8.1 question 18

Answers (1)

Answer: k=2

Hint:

For a function to be continuous at a point, its LHL RHL and value at that point should be equal.

Solution:

Given,  

                f(x)=\left(\begin{array}{c} \frac{x^{2}-1}{x-1}, \text { if } x \neq 1 \\\\ k, \text { if } x=1 \end{array}\right)

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

               \lim _{x \rightarrow 1} f(x)=f(1)

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

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

              k=2

               

              

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