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Question Number 72688 by Rio Michael last updated on 31/Oct/19

$$Evaluate$$$$\underset{t\to 9}{lim}\frac{9-t}{3-\sqrt{t}}$$

Answered by JDamian last updated on 01/Nov/19

$$\underset{t\to 9}{\lim }\left(\frac{9-t}{3-\sqrt{t}}\times \frac{3+\sqrt{t}}{3+\sqrt{t}}\right)=\underset{t\to 9}{\lim }\frac{(9-t)(3+\sqrt{t})}{9-t}=$$$$=\underset{t\to 9}{\lim }(3+\sqrt{t})=6$$

Commented by Rio Michael last updated on 31/Oct/19

$$thankssir$$

Answered by malwaan last updated on 31/Oct/19

$$\mathit{p}\mathit{u}\mathit{t}\mathit{t}={\mathit{x}}^2$$$$\Rightarrow \underset{\mathit{x}\to 3}{\mathit{l}\mathit{i}\mathit{m}}\frac{9-{\mathit{x}}^2}{3-\mathit{x}}$$$$=\underset{\mathit{x}\to 3}{\mathit{l}\mathit{i}\mathit{m}}\frac{(3+\mathit{x})(3-\mathit{x})}{3-\mathit{x}}$$$$=\underset{\mathit{x}\to 3}{\mathit{l}\mathit{i}\mathit{m}}(3+\mathit{x})=3+3=6$$

Answered by petrochengula last updated on 01/Nov/19

$$={\lim }_{\mathrm{t}\to 9}\frac{(3-\sqrt{\mathrm{t}})(3+\sqrt{\mathrm{t}})}{3-\sqrt{\mathrm{t}}}={\lim }_{\mathrm{t}\to 9}(3+\sqrt{\mathrm{t}})=6$$

Commented by Rio Michael last updated on 01/Nov/19

$$thanks$$

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