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  • need solution for RD Sharma maths class 12 chapter 8 Continuity exercise Fill in the blanks question 3

need solution for RD Sharma maths class 12 chapter 8 Continuity exercise Fill in the blanks question 3

Answers (1)

Answer: 2
Hint: You must know about the concept of continuous function
Given:

            f(x)=\left\{\begin{array}{l} a x^{2}-b, 0 \leq x<1 \\ 2, x=1 \\ x+1,1<x \leq 2 \end{array} \quad \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)=\lim _{x \rightarrow 1^{+}} f(x)=\lim _{x \rightarrow 1} f(x) \\ \\&\lim _{x \rightarrow 1^{-}} a x^{2}-b=\lim _{x \rightarrow 1^{+}} x+1=\lim _{x \rightarrow 1} 2 \end{aligned}

                \lim _{h \rightarrow 0} a(1-h)^{2}-b=\lim _{h \rightarrow 0}(1+h)+1=\lim _{x \rightarrow 1} 2

                \begin{aligned} &a-b=2=2 \\ &a-b=2 \end{aligned}

               

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