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  • Please solve RD Sharma class 12 chapter 8 Continuity exercise Fill in the blanks question 1 maths textbook solution

Please solve RD Sharma class 12 chapter 8 Continuity exercise Fill in the blanks question 1 maths textbook solution

Answers (1)

Answer: 3a^{2}

Hint:

            Use the formula (x^{3}-a^{3}) so that f(x)\neq \frac{0}{0} at x\neq a

Given:

            f(x)=\left\{\begin{array}{cl} \frac{x^{3}-a^{3}}{x-a} & , x \neq a \\ b & , x=a \end{array}\right.   is continuous at x=a

Solution:

                If f(x) is continuous at x=a , then RHL= LHL

                LHL,

                \begin{aligned} &\lim _{x \rightarrow a^{-}} f(x)=\lim _{x \rightarrow a} \frac{x^{3}-a^{3}}{x-a} \\ &=\lim _{x \rightarrow a^{-}} \frac{(x-a)\left(x^{2}+a x+a^{2}\right)}{(x-a)} \\ &=\lim _{x \rightarrow a^{-}} x^{2}+a x+a^{2} \\ &=\lim _{\mathbb{\Xi} \rightarrow 0} a^{2}+a^{2}+a^{2} \\ &=3 a^{2} \end{aligned}\left [ \because x=a \right ]

                RHL,

                \begin{aligned} &\lim _{x \rightarrow a^{+}} f(x)=\lim _{x \rightarrow a^{+}} b \\ &=b \end{aligned}

                As f(x) is continuous at x=a, RHL = LHL

                    b=3a^{2}

 

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