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  • Explain solution RD Sharma class 12 chapter 8 Continuity exercise multiple choice question 32 maths

Explain solution RD Sharma class 12 chapter 8 Continuity exercise multiple choice question 32 maths

Answers (1)

Answer:

 The correct option is (d)

Hint:

 A function f(x) is said to be continuous at a point x = a of its domain, if

\lim _{x \rightarrow a^{+}} f(a+h)=\lim _{x \rightarrow a^{-}} f(a-h)=f(a)

Given:

 f(x)= \begin{cases}a x^{2}+b & , 0 \leq x<1 \\ 4 & , \quad x=1 \\ x+3 &, 1<x \leq 2\end{cases}

Step 1: Understand that, f(x) is continuous at x = 1

Therefore,

\begin{aligned} &\therefore \lim _{h \rightarrow 0} f(x)=f(1) \\ &\lim _{h \rightarrow 0} f(1-h)=4 \\ &\lim _{h \rightarrow 0} a(1-h)^{2}+b=4 \end{aligned}

Therefore, the possible values for (a, b) can be (2, 2), (3, 1), (4, 0) but (a,b) ≠ (5, 2)

Hence, the correct answer is option (d).

Posted by

Gurleen Kaur

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