Maclaurin Series Expansion help

This is the given problem, ive tried watching in youtube but the one they have is taylor series, i just dont understand the e_a falls below below a prespecified error criterion es, im using the 2013a matlab which doesnt support the function maclaurin. thank you

[David Goodmanson]

Hi Dean

A Taylor series is an expansion in nonnegatve powers of (x-a). In the special case a=0 it is a Taylor series expansion in powers of z, which is also called a Maclauren series, which is what you have. So you can just call it a Taylor series.

I think they want you to come up with an e_s so that as you increase the number of terms in the Taylor series, once the the exact answer and the Taylor series answer agree with e_s, they also agree to four significant figures.

[Walter Roberson]

maclaurin is just taylor expansion around x = 0

[Dean Yankee Jabili]

thank you for making it clear to me

[Walter Roberson]

https://mathworld.wolfram.com/MaclaurinSeries.html