# 3.4.6 limit of a power function

#### karush

##### Well-known member

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

#### Prove It

##### Well-known member
MHB Math Helper
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

##### Well-known member
Ok I see what you mean
But there is no graph on the positive side

also its 2 not 1

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#### HallsofIvy

##### Well-known member
MHB Math Helper
What do you mean "there is no graph on the positive side"? Of couse there is.

#### topsquark

##### Well-known member
MHB Math Helper
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 $$\displaystyle x \geq 2$$. (Why does it "disappear?" Why does it "reappear?")

-Dan

#### karush

##### Well-known member
actually I don't know why it does not graph $0\le x \le 2$

#### Prove It

##### Well-known member
MHB Math Helper
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

##### Well-known member
MHB Math Helper
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.[/FONT]