Find a power series for the function centered at 0.

Name: Find a power series for the function centered at 0.
Brand: Quizplus
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Question

Find a power series for the function  centered at 0.

Quizplus · Accepted Answer

To find the power series of a function centered at 0, we can use the formula:

f(x) = a0 + a1(x) + a2(x^2) + a3(x^3) + ...

where 
a0 = f(0) 
an = f^(n)(0) / n!

Here, f(x) = 11e^x. 
So, 
a0 = f(0) = 11e^0 = 11 
an = f^(n)(0) / n! = e^0 / n! = 1/n!

Therefore, the power series is: 
11 + x + (x^2)/2! + (x^3)/3! + ...

which can be simplified to: 
11e^x

Find a Power Series for the Function Centered at 0