Question

expand (1+2x)^1/4 till
x^3

Answer 1

then i need to find the estimate of 4root of 18 and by substituting x=1/16

Answer 2

the question is a little bit confusing....

Answer 3

it's asking for the taylor series expansion, i assume. and i'm also assuming at x=0.

so if f(x) = (1 + 2x)^(1/4):

f(0) = 1, f'(0) = 1/2, f"(0) = -3/4, f3(0) = 21/8

thus (1 + 2x)^(1/4) is roughly equal to 1 + x/2 - (3/8)x^2 + (7/16)x^3

substituting x = 1/16 will give a nice approximation for (9/8)^(1/4), but i don't see how it will give a nice approximation for 4*sqrt(18)