Calculus 2: Maclaurin Series

Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function

Here is Table 1: https://webassign.net/scalcet/11-10-030.gif

Given function: f(x) = e^x + e^(2x)

So according to Table 1 I already have the e^x part, so now I just need e^(2x). With e^(2x) I rewrote it as (e^x)^2 which will give me a (summation)^2. My question is, is it okay to rewrite e^(2x) as (e^x)^2 and start off from there?

Question

Calculus 2: Maclaurin Series

Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function

Here is Table 1: https://webassign.net/scalcet/11-10-030.gif

Given function: f(x) = e^x + e^(2x)

So according to Table 1 I already have the e^x part, so now I just need e^(2x). With e^(2x) I rewrote it as (e^x)^2 which will give me a (summation)^2. My question is, is it okay to rewrite e^(2x) as (e^x)^2 and start off from there?

tkhunny · Answer

Why would you make such a revision?

If $f(x) = e^{x}$, then $f(2x) = e^{2x}$

anonymous · Answer

So I assume that I can't write e^(2x) as (e^x)^2?

tkhunny · Answer

You can if you want, but again, why would you do that?

Find the MacLaurin Series for f(x) = e^x

Once you have that, using what you just wrote about f(x) and its series expansion, write f(2x) and you are nearly done.