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Question Number 89922 by student work last updated on 20/Apr/20

Commented by john santu last updated on 20/Apr/20

$$\underset{x\to 0}{\lim }\sqrt{5-2x^2}⩽\underset{x\to 0}{\lim }f\left(x\right)⩽\underset{x\to 0}{\lim }\sqrt{5+2x^2}$$$$\left(1\right)\underset{x\to 0}{\lim }\sqrt{5-2x^2}=\sqrt{5}$$$$\left(2\right)\underset{x\to 0}{\lim }\sqrt{5+2x^2}=\sqrt{5}$$$$then\underset{x\to 0}{\lim }f\left(x\right)=\sqrt{5}$$

Commented by jagoll last updated on 20/Apr/20

$$\sqrt{5}\underset{x\to 0}{\lim }\mathrm{f}\left(\mathrm{x}\right)=\sqrt{5}\times \sqrt{5}=5$$

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