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प्रश्न
Let \[f\left( x \right) = \left\{ \begin{array}\\ \frac{x - 4}{\left| x - 4 \right|} + a, & x < 4 \\ a + b , & x = 4 \\ \frac{x - 4}{\left| x - 4 \right|} + b, & x > 4\end{array} . \right.\]Then, f (x) is continuous at x = 4 when
पर्याय
a = 0, b = 0
a = 1, b = 1
a = −1, b = 1
a = 1, b = −1.
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उत्तर
a = 1, b = −1.
Given:
We have
(LHL at x = 4) =
(RHL at x = 4) = \[\lim_{x \to 4^+} f\left( x \right) = \lim_{h \to 0} f\left( 4 + h \right)\]
Also,
If f(x) is continuous at x = 4, then
\[\lim_{x \to 4^-} f\left( x \right) = \lim_{x \to 4^+} f\left( x \right) = f\left( 4 \right)\]
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