Find the terms through degree four of the Maclaurin series of $f(x)$.
$$f(x) = \frac{1}{1+\sin x}$$
My work:
The Maclaurin series for $\sin x$ up to degree $4$ is $x – \frac{x^3}{6} + \frac{x^5}{120}$
The Maclaurin series for $\frac{1}{1+x}$ up to degree $4$ is $1 – x + x^2 – x^3 + x^4$
I substituted $x – \frac{x^3}{6} + \frac{x^5}{120}$ for $x$ in $1 – x + x^2 – x^3 + x^4$
Did I do this right?
Plugging this into WolframAlpha, I get this: http://goo.gl/SKddyh
Which doesn't seem like the answer in the text: $1-x+x^2-\frac{5x^3}{6}+\frac{2x^4}{3}$
Best Answer
Have a look at this:
Your equation, expanded
As you can see, what you plugged into WolframAlpha was the same equation as the answer in the text.