JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If the function \(f\left( x \right) = \left\{ \begin{array}{l}
a\,\left| {\pi - x} \right|\, + 1,\,\,x \le 5\,\\
b\,\,\left| {\pi - x} \right|\, + 3,\,\,x > 5\,\,
\end{array} \right.\) is continuous at \(x = 5\), then the value of \(a -b\) is
- A \(\frac{2}{{5 - \pi }}\)
- B \(\frac{2}{{\pi - 5}}\)
- C \(\frac{2}{{\pi + 5}}\)
- D \(\frac{-2}{{\pi + 5}}\)
Answer & Solution
Correct Answer
(A) \(\frac{2}{{5 - \pi }}\)
Step-by-step Solution
Detailed explanation
\(f\left( x \right) = \left\{ \begin{array}{l} a\left| {\pi - x} \right| + 1,x \le 5\\ b\left| {\pi - x} \right| + 3,x > 5 \end{array} \right.\) Contributes at \(x=5\) \(\therefore L.H.L. = R.H.L = f\left( 5 \right)\)…
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