Question
6. Déterminez les trois premiers termes non nuls de la série de Maclaurin de .
Studdy Solution
STEP 1
What is this asking?
We need to find the first three *non-zero* terms of the Maclaurin series for the function .
Watch out!
Remember that the Maclaurin series is just a Taylor series centered at .
Don't forget to multiply the series for by *after* expanding !
STEP 2
1. Expand as a Maclaurin series.
2. Multiply the series by .
3. Simplify and identify the first three non-zero terms.
STEP 3
The Maclaurin series for is given by This is a super famous series, so it's really useful to remember!
STEP 4
Let's write out the first few terms of the series: We'll use these terms in the next step.
STEP 5
Now, we multiply the expanded series by :
STEP 6
Now, let's combine the like terms:
STEP 7
The first three **non-zero** terms are , , and .
STEP 8
The first three non-zero terms of the Maclaurin series for are , which corresponds to answer choice A.
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