JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f :R \to R\) be a function defined as \(f\left( x \right) = \left\{ \begin{array}{l}
5,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,if\,\,\,\,\,\,\,x \le 1\,\,\,\,\,\,\,\\
a + bx,\,\,\,\,if\,\,\,\,\,\,1 < x < 3\\
b + 5x,\,\,\,\,if\,\,\,\,\,\,3 \le x < 5\\
30,\,\,\,\,\,\,\,\,\,\,if\,\,\,\,\,\,\,x \ge 5
\end{array} \right.\,\,\,\,\) Then \(f\) is
- A continuous if \(a = 5\) and \(b = 5\)
- B continuous if \(a = 5\) and \(b = 10\)
- C continuous if \(a = 0\) and \(b = 5\)
- D not continuous for any values of \(a\) and \(b\)
Answer & Solution
Correct Answer
(D) not continuous for any values of \(a\) and \(b\)
Step-by-step Solution
Detailed explanation
For \(x=1\) \(R.H.L=a+b\) \(L.H.L=5\) So to be continuous at \(x=1\) \(a+b=5\) ..........\((i)\) for \(x=3\) \(R.H.L=b+15\) \(L.H.L=a+3b\) \(b+15=a+3b\) \(a+2b=15\) ........\((ii)\) for \(x=5\) \(R.H.L=30\) \(L.H.L=b+25\) \(b+25=30\) \(b=5\). From equation \((ii)\) \(a=10\) but…
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