# How do you find the maclaurin series expansion of f(x)=cos3x?

Refer to explanation

Don't use plagiarized sources. Get Your Custom Essay on
How do you find the maclaurin series expansion of f(x)=cos3x?
Just from \$13/Page

A Maclaurin series is a Taylor series expansion of a function about 0,
hence

##f(x)=f(0)+f'(0)x+(f”(0))/(2!)*x^2+(f”'(0))/(3!)+…+(f^(n)(0))/(n!)*x^n##

where ##f^(n)(0)## is the n-th order derivative of ##f(x)##.

Hence we have to calculate some derivatives around zero so

##f(x)=cos3x=>f(0)=1##
##f'(x)=-3sin3x=>f'(0)=0##
##f”(x)=-3^2*cos3x=>f”(0)=-3^2##
##f”'(x)=3^3*sin3x=>f”'(0)=0##
##f””(4)=3^4*cos3x=>f””(0)=3^4##

So the maclaurin series can be written as

##cos3x=Σ_0^oo (-1)^n*(3)^(2n)*(x^(2n))/((2n)!)##

## Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
\$26
The price is based on these factors:
Number of pages
Urgency
Basic features
• Free title page and bibliography
• Unlimited revisions
• Plagiarism-free guarantee
• Money-back guarantee
On-demand options
• Writer’s samples
• Part-by-part delivery
• Overnight delivery
• Copies of used sources
Paper format
• 275 words per page
• 12 pt Arial/Times New Roman
• Double line spacing
• Any citation style (APA, MLA, Chicago/Turabian, Harvard)

# Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

### Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

### Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

### Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.