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  • Please Solve RD Sharma Class 12 Chapter 8 Continuity Exercise 8.1 Question 21 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 8 Continuity Exercise 8.1 Question 21 Maths Textbook Solution.

Answers (1)

Answer:

                k=\frac{3}{4}

Hint:

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

Given:

                f(x)=\left(\begin{array}{r} k x^{2}, \text { if } x \leq 2 \\\\ 3, \text { if } x>2 \end{array}\right)   is continuous at  x=2

Solution:

                f(x)=\left(\begin{array}{r} k x^{2}, \text { if } x \leq 2 \\\\ 3, \text { if } x>2 \end{array}\right)

If f\left ( x \right ) is continuous at x=2 , then

                 \begin{aligned} &\lim _{x \rightarrow 2^{-}} f(x)=\lim _{x \rightarrow 2^{+}} f(x)=f(2) \\\\ &\lim _{x \rightarrow 2^{-}} f(x)=\lim _{h \rightarrow 0} f(2-h)=\lim _{h \rightarrow 0} k(2-h)^{2}=4 k \end{aligned}

                \begin{aligned} &f(2)=3 \\ &4 k=3 \\ &k=\frac{3}{4} \end{aligned}

               

               

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