यदि $f(x) = \left\{ \begin{array}{l}a{x^2} - b,\,\,when\,\,{\rm{\,\, }}0 \le x < 1\\\,\,\,\,\,\,\,\,\,\,\,\,\,2,\;\,when\,\,{\rm{ }}x = 1\\\,\,\,\,\,x + 1,\,\,\,when\,{\rm{ \,\,1}} \,\, < x \le 2\end{array} \right.$, $x = 1$ पर सतत् है तो $a, b$ के अधिक उपयुक्त मान होंगे
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Answer
$\mathop {\lim }\limits_{x \to 1 - } f(x) = a - b,\mathop {\lim }\limits_{x \to 1 + } f(x) = 2$
$\Rightarrow a - b = 2$
अत: सभी $a, b$ के मानों के लिए $f(x) , x=1$ पर सतत् है।
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