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  • need solution for RD Sharma maths class 12 chapter 8 Continuity exercise Fill in the blanks question 15

need solution for RD Sharma maths class 12 chapter 8 Continuity exercise Fill in the blanks question 15

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Answer: 2

Hint: f(x)  is continuous when LHL=RHL

Given: f(x)=\left\{\begin{aligned} a x+1, & \text { if } x \geq 1 \\ x+2, & \text { if } x<1 \end{aligned}\right.

Solution:

            f(x)=\left\{\begin{aligned} a x+1, & \text { if } x \geq 1 \\ x+2, & \text { if } x<1 \end{aligned}\right.

            f(x)  is continuous when LHL=RHL

            \lim _{x \rightarrow 1^{+}} a x+1=\lim _{x \rightarrow 1^{-}} x+2 \text { at } x=1

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

            \begin{aligned} &a+1=3 \\ &a=2 \end{aligned}

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