MHB How to Find the Limit of a Power Function Using Desmos?

[karush]

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Ok all I did was DesmosNot real sure how to take limit
View attachment 9665

 

[Prove It]

Ok all I did was DesmosNot real sure how to take limit

Why are you plugging in large negative values for x? Surely for an infinite limit you should be plugging in large positive values.

As for a hint, you should use the standard limit $\displaystyle \lim_{x \to \infty} \left( 1 + \frac{1}{x} \right) ^x = \mathbf{e} $.

 

[karush]

Ok I see what you mean
But there is no graph on the positive side

also its 2 not 1

 

[HallsofIvy]

What do you mean "there is no graph on the positive side"? Of couse there is.

 

[topsquark]

Ok I see what you mean
But there is no graph on the positive side

also its 2 not 1

Prove It is not giving you the answer he is giving you a suggestion that you can use the limit he posted. See if there is any kind of substitution you can make to put your limit into the form he gave you.

And the graph of f(x) becomes real again for [math]x \geq 2[/math]. (Why does it "disappear?" Why does it "reappear?")

-Dan

 

[karush]

actually I don't know why it does not graph $0\le x \le 2$

 

[Prove It]

actually I don't know why it does not graph $0\le x \le 2$

Look at the numbers. Can you divide by 0? Can you take an even root of a negative number?

 

[HallsofIvy]

For this problem it doesn't matter that "it does't graph" between 0 and 2!

Using the "Desmos graphing calculator" at [FONT=Verdana,Arial,Tahoma,Calibri,Geneva,sans-serif]https://www.desmos.com/calculator you can look at the graph at very large x and small values of y so get an idea of the values you need.