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  • Please Solve RD Sharma Class 12 Chapter 8 Continuity Exercise 8.1 Question 36 subquestion (vii) Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 8 Continuity Exercise 8.1 Question 36 subquestion (vii) Maths Textbook Solution.

Answers (1)

Answer:

                k=4

Hint:

f(x)  must be defined. The limit of the f(x) approaches the value x must exist.

Given:

                f(x)=\left(\begin{array}{c} k x^{2}, x \geq 1 \\ 4, x<1 \end{array}\right)

Solution:

                f(x)=\left(\begin{array}{c} k x^{2}, x \geq 1 \\ 4, x<1 \end{array}\right)

We have

(LHL at  x=1 )

                \lim _{x \rightarrow 1^{-}} f(x)=\lim _{h \rightarrow 0} f(1-h)=\lim _{h \rightarrow 0} 4=4

(RHL at  x=1 )

                \lim _{x \rightarrow 1^{+}} f(x)=\lim _{h \rightarrow 0} f(1+h)=\lim _{h \rightarrow 0} k(1+h)^{2}=k

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

                \begin{aligned} &\lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1^{+}} f(x) \\ &k=4 \end{aligned}

               

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