Maclaurin series problem?

Question

find the maclaurin series of f(x)=sqrt(1+x^2) up to term containing x^2

then find sqrt(1.16)

Answer 1

The maclaurin series expansion of f(x) is:

f(x) = f(0) + x*f '(0) + (x^2/2!)*f ''(0) + (x^3/3!)*f '''(0) + ...

In this case,

f(0) = 1

f '(0) = 0

f ''(0) = 1

so

f(x) = 1 + x^2/2 + ...

Therefore, the expansion up to the x^2 term is

1 + x^2/2

and so an estimate for sqrt(1.16) is:

f(0.4) = 1 + .16/2 = 1.08

Answer 2

sorry!!! i wasn't in class when this was lectured.

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