School and Work

The approximation e˜ 1+1+(1/2)+(1/6)= (8/3) is obtained from the first four terms of the Maclaurin
expansion of e^x , x = 1. From the Taylor Remainder Theorem, which of the following is the guaranteed
maximum absolute value of the error, |Rn|, of this approximation (you may take it as known that e = 3).

a. (1/24)
b. (1/8)
c. (1/6)
d. 0
e. infinity
f. 1

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I am having trouble how to do this:

Evaluate this limit using Taylor series:

lim x-->0 ((2cos2x - 2 + 4x^2)/2x^4) . This is 0/0 and you can use l'Hopital's rule but I am not supposed to as I am supposed to use Taylor series. Can anyone help me with a step-by-step?

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