1. ## exponential question

Can someone explain the difference between:

$\displaystyle e^{(x^2)}$ and $\displaystyle e^{x^2}$

I'm sure it is a simple answer, but as my Calc II final is tomorrow, I'm practically brain dead
Thanks!

2. Other than that $\displaystyle e^{x^2}$ might be taken for $\displaystyle (e^x)^2$ when typed as text, I'm not sure there is a difference.

3. Originally Posted by stapel
Other than that $\displaystyle e^{x^2}$ might be taken for $\displaystyle (e^x)^2$ when typed as text, I'm not sure there is a difference.

Their graphs are different, that is why I ask. Here is how I put them into my calculator:

y = e^(x)^2 *this one looks like your run of the mill exponential compressed vertically

y = e^(x^2) *this one looks like a vertically compressed parabola, vertex @ (0,1)

I just need to know because I'm pretty sure I'll see it tomorrow on my final in the volumes of rotation section

4. Originally Posted by mollymcf2009
Their graphs are different, that is why I ask. Here is how I put them into my calculator:

y = e^(x)^2 *this one looks like your run of the mill exponential compressed vertically

your calculator is interpreting this syntax as e^(2x)

y = e^(x^2) *this one looks like a vertically compressed parabola, vertex @ (0,1)

I just need to know because I'm pretty sure I'll see it tomorrow on my final in the volumes of rotation section
.

5. Ok, this is the problem:

Consider the region bounded by the curves:

$\displaystyle y = e^{x^2}$ ........ etc. etc.

So, how do I interpret that? No parentheses anywhere. What does this graph look like?

6. ## I think I've got it

Ok, So I'm assuming that since like Skeeter said $\displaystyle e^{(x^2)}$ is being interpreted at $\displaystyle e^{(2x)}$ that the graph of $\displaystyle e^{x^2}$ looks like $\displaystyle e^x$ but compressed vertically is the correct graph.

7. Originally Posted by mollymcf2009
Ok, So I'm assuming that since like Skeeter said $\displaystyle e^{(x^2)}$ is being interpreted at $\displaystyle e^{(2x)}$ that the graph of $\displaystyle e^{x^2}$ looks like $\displaystyle e^x$ but compressed vertically is the correct graph.
that's not what I said ... e^(x)^2 is interpreted as e^(2x) by the calculator, because the calculator sees the expression as the quantity (e^x) squared

e^(x^2) is the correct calculator syntax for the desired even function, $\displaystyle e^{x^2}$.

8. Originally Posted by skeeter
that's not what I said ... e^(x)^2 is interpreted as e^(2x) by the calculator, because the calculator sees the expression as the quantity (e^x) squared

e^(x^2) is the correct calculator syntax for the desired even function, $\displaystyle e^{x^2}$.
Ok, sorry, I guess I just read it wrong. Thanks for clarifying! So the graph DOES look like a compressed parabola. Glad you caught me on that!

9. Molly

Good Luck on your Final tommorow