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Question Number 46060 by samitoh last updated on 20/Oct/18

$$determinewhetherornot\underset{\mathrm{x}\to 0}{\lim }[$$$$iscontinuous$$

Answered by tanmay.chaudhury50@gmail.com last updated on 20/Oct/18

$$afunctionf\left(x\right)willbecontinuousatx=a$$$$when\underset{x\to a-}{\lim }f\left(x\right)=\underset{x\to a+}{\lim }f\left(x\right)=f\left(a\right)$$$$\underset{x\to 4-}{\lim }f\left(x\right)$$$$=\underset{x\to 4-}{\lim }\frac{x^2-16}{x-4}$$$$=\underset{x\to 4-}{\lim }\frac{(x+4)(x-4)}{x-4}=4+4=8$$$$\underset{x\to 4+}{\lim }f\left(x\right)$$$$=\underset{x\to 4+}{\lim }\frac{x^2-16}{x-4}$$$$=\underset{x\to 4+}{\lim }\frac{(x+4)(x-4)}{x-4}=4+4=8$$$$f\left(4\right)=8sof\left(x\right)continuousatx=4$$$$$$

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