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Question Number 82607 by arthur.kangdani@gmail.com last updated on 23/Feb/20

Commented by jagoll last updated on 23/Feb/20

$$\underset{x\to 2}{\lim }\frac{4-x^2}{4-x^2}\times \underset{x\to 2}{\lim }3+\sqrt{x^2+5}=1\times 6=6$$

Commented by niroj last updated on 23/Feb/20

$$\mathrm{yes}\mathrm{my}\mathrm{friend}\mathrm{your}\mathrm{saying}\mathrm{true}.$$$$\mathrm{its}\mathrm{been}\mathrm{error}\mathrm{by}\mathrm{the}\mathrm{wrong}\lim$$$$\mathrm{now}\mathrm{done}.$$

Commented by jagoll last updated on 23/Feb/20

$$notcorrect.howyougot$$$$2\sqrt{2^2+5}=2\sqrt{14}?$$

Commented by jagoll last updated on 23/Feb/20

$$thisequation\underset{x\to 2}{\lim }not\underset{x\to 3}{\lim }$$

Commented by mathmax by abdo last updated on 23/Feb/20

$$={lim}_{x\to 2}\frac{(4-x^2)(3+\sqrt{x^2+5})}{9-x^2-5}={lim}_{x\to 2}\frac{(4-x^2)(3+\sqrt{x^2+5})}{4-x^2}$$$$={lim}_{x\to 2}(3+\sqrt{x^2+5})=6$$

Answered by niroj last updated on 23/Feb/20

$$$$$$$$$$\underset{\mathrm{x}\to 2}{\stackrel{\lim }{}}\frac{4-{\mathrm{x}}^2}{3-\sqrt{{\mathrm{x}}^2+5}}$$$$=\underset{\mathrm{x}\to 2}{\stackrel{\lim }{}}\frac{-2\mathrm{x}}{\frac{-2\mathrm{x}}{2\sqrt{{\mathrm{x}}^2+5}}}=\underset{\mathrm{x}\to 2}{\stackrel{\lim }{}}2\sqrt{{\mathrm{x}}^2+5}$$$$=2\sqrt{2^2+5}=2\sqrt{9}=2.3=6//.$$

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