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  • explain solution RD Sharma class 12 chapter 8 Continuity exercise Fill in the blanks question 4 maths

explain solution RD Sharma class 12 chapter 8 Continuity exercise Fill in the blanks question 4 maths

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Answer: 1
Hint: If f(x)is continuous, then all the functions are equal
Given:

                f(x)=\left\{\begin{array}{l} x+k, x<3 \\ 4, x=3 \quad \text { is continuous at } x=3 \\ 3 x-5, x>3 \end{array}\right.
Solution:

                We know that as function is continuous at x=3 ,

                    \begin{aligned} &\lim _{x \rightarrow 3^{-}} f(x)=\lim _{x \rightarrow 3^{+}} f(x)=\lim _{x \rightarrow 3} f(x) \\\\ &\lim _{x \rightarrow 3^{-}} x+k=\lim _{x \rightarrow 3^{+}} 3 x-5=\lim _{x \rightarrow 3} 4 \end{aligned}

                    \lim _{h \rightarrow 0}(3-h)+k=\lim _{h \rightarrow 0} 3(3+h)-5=\lim _{x \rightarrow 3} 4

                 \begin{aligned} &3+k=3(3)-5=4 \\ &3+k=4=4 \\ &k=1 \end{aligned}

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