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  • Explain solution RD Sharma class 12 Chapter 8 Continuity exercise 8.1 question 46

Explain solution RD Sharma class 12 Chapter 8 Continuity exercise 8.1 question 46

Answers (1)

Answer:

                3a-3b=2

Hint:

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

Given:

                f(x)=\left\{\begin{array}{l} a x+1, \text { if } x \leq 3 \\ b x+3, \text { if } x>3 \end{array}\right.

Solution:

                f(x)=\left\{\begin{array}{l} a x+1, \text { if } x \leq 3 \\ b x+3, \text { if } x>3 \end{array}\right.

We have

(LHL at  x=3 )

                \lim _{x \rightarrow 3^{-}} f(x)=\lim _{h \rightarrow 0} f(3-h)=\lim _{h \rightarrow 0}[a(3-h)+1]=3 a+1

(RHL at x=3  )

                \lim _{x \rightarrow 3^{+}} f(x)=\lim _{h \rightarrow 0} f(3+h)=\lim _{h \rightarrow 0}[b(3+h)+3]=3 b+3

Also  f(2)=k

If f\left ( x \right )  is continuous at x=3 .

\begin{aligned} &\lim _{x \rightarrow 3^{+}} f(x)=\lim _{x \rightarrow 3^{-}} f(x) \\ &3 a+1=3 b+3 \\ &3 a-3 b=2 \end{aligned}

Hence the required relationship between a \; and \; i \; is \; 3 a-3 b=2

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