# exponential question

• Apr 28th 2009, 04:01 PM
mollymcf2009
exponential question
Can someone explain the difference between:

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

I'm sure it is a simple answer, but as my Calc II final is tomorrow, I'm practically brain dead
Thanks!
• Apr 28th 2009, 04:06 PM
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. (Wondering)
• Apr 28th 2009, 04:10 PM
mollymcf2009
Quote:

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. (Wondering)

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 :)
• Apr 28th 2009, 04:14 PM
skeeter
Quote:

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 :)

.
• Apr 28th 2009, 04:20 PM
mollymcf2009
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?
• Apr 28th 2009, 04:33 PM
mollymcf2009
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.
• Apr 28th 2009, 05:13 PM
skeeter
Quote:

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}\$.
• Apr 28th 2009, 05:30 PM
mollymcf2009
Quote:

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! (Wink)
• Apr 28th 2009, 08:49 PM
Calculus26
Molly

Good Luck on your Final tommorow