Question

What is the limit, using the Taylor series: lim as x approaches zero, ((sqrt (1+x))-1-(x/2)) / 4x^2

Answer 1

do you know the taylor series for \(\sqrt{1+x}\) ?

Answer 2

actually you only need the first three terms

Answer 3

\[\sqrt{1+x}=1+\frac{x}{2}-\frac{x^2}{8}\] subtracting leaves \(-\frac{x^2}{8}\)

Answer 4

then divide by \(4x^2\) and that will be your limit

Answer 5

alright, I have not used this site before. I am looking it over. Thanks a lot I have many challenging calc II questions

Answer 6

you got this? when you divide you get a constant
all other higher powers will contain \(x^k\) so when you let \(x=0\) they are gone and you are left only with the constant