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Hi Ho!

Mmmm... I have a problem with this one:

[itex]\lim_{x\rightarrow-\infty} \frac{x}{\sqrt{z^2+x^2}}[/itex]

Using a computer graphics tool, I found that the result should be -1 by looking at the generated graph.

But if I do it by hands, I find 1 as follows:

[itex]\lim_{x\rightarrow-\infty} \frac{x}{\sqrt{z^2+x^2}} = \lim_{x\rightarrow-\infty} \frac{x \frac{1}{x}}{\sqrt{z^2+x^2} \frac{1}{x}}[/itex]

[itex]= \lim_{x\rightarrow-\infty} \frac{1}{\sqrt{\frac{z^2+x^2}{x^2}}}[/itex]

[itex]= \lim_{x\rightarrow-\infty} \frac{1}{\sqrt{1+(\frac{z}{x})^2}}[/itex]

[itex]= \frac{1}{\sqrt{1+(\frac{z}{-\infty})^2}}[/itex]

[itex]= \frac{1}{\sqrt{1+0}}[/itex]

[itex]= \frac{1}{1}[/itex]

[itex]= 1[/itex]

Would you please correct my mistake?

Thank you very much!

Mmmm... I have a problem with this one:

[itex]\lim_{x\rightarrow-\infty} \frac{x}{\sqrt{z^2+x^2}}[/itex]

Using a computer graphics tool, I found that the result should be -1 by looking at the generated graph.

But if I do it by hands, I find 1 as follows:

[itex]\lim_{x\rightarrow-\infty} \frac{x}{\sqrt{z^2+x^2}} = \lim_{x\rightarrow-\infty} \frac{x \frac{1}{x}}{\sqrt{z^2+x^2} \frac{1}{x}}[/itex]

[itex]= \lim_{x\rightarrow-\infty} \frac{1}{\sqrt{\frac{z^2+x^2}{x^2}}}[/itex]

[itex]= \lim_{x\rightarrow-\infty} \frac{1}{\sqrt{1+(\frac{z}{x})^2}}[/itex]

[itex]= \frac{1}{\sqrt{1+(\frac{z}{-\infty})^2}}[/itex]

[itex]= \frac{1}{\sqrt{1+0}}[/itex]

[itex]= \frac{1}{1}[/itex]

[itex]= 1[/itex]

Would you please correct my mistake?

Thank you very much!

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