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  • Provide solution for RD Sharma maths class 12 chapter Continuity exercise 8.2 question 7

Provide solution for RD Sharma maths class 12 chapter Continuity exercise 8.2 question 7

Answers (1)

Answer:

 a = 3,  b = -2

Hint:

 Put at LHL = RHL at x = 2, x = 4

Given:

 f(x)= \begin{cases}x^{2}+a x+b & 0 \leq x<2 \\ 3 x+2 & 2 \leq x \leq 4 \\ 2 a x+5 b & 4<x \leq 8\end{cases}

Explanation:

At x = 2

\begin{aligned} &L . H . L=R . H . L=f(2) \qquad \qquad \qquad...(A)\\ &f(2)=3 \times 2+2=8 \qquad \qquad \qquad...(1)\\ &\text { L.H. } L=\lim _{x \rightarrow 2^{-}} f(x)=\lim _{h \rightarrow 0}(2-h)\\ &=\lim _{h \rightarrow 0}(2-h)^{2}+a(2-h)+b\\ &=4+2 a+b \end{aligned}

from (B)

\begin{aligned} &4+2 a+b=8\\ &\Rightarrow 2 a+b=4 \qquad \ldots(B)\\ &\text { Now at } x=4\\ &L . H . L=R . H . L=f(4) \quad \ldots (C)\\ &f(4)=3 \times 4+2=8 \quad \ldots (2) \end{aligned}

\begin{aligned} &R . H . L=\lim _{x \rightarrow 4^{+}} f(x)=\lim _{h \rightarrow 0}(4+h) \\ &=\lim _{h \rightarrow 0} 2 a(4+h)+5 b=8 b+5 h \end{aligned}

From (C)

8 b+5 h=14 \quad \dots(D)

Solving (B) & (D) we get

Hence, a = 3, b = -2

Posted by

Gurleen Kaur

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