Binomial Expansion

Hey,
Struggling with this question:
Expand (1-2x)^5 to give a quadratic approximation for small values of x then by setting x=0.01 into approximation, find approx value of 0.98^5 and calculate percentage error in this approximation
Done the expansion okay but don't understand how to approximate it and do the second half of the question?
Thanks :smile:

Reply 1

mqb2766

21

Original post by lau321

Hey,
Struggling with this question:
Expand (1-2x)^5 to give a quadratic approximation for small values of x then by setting x=0.01 into approximation, find approx value of 0.98^5 and calculate percentage error in this approximation
Done the expansion okay but don't understand how to approximate it and do the second half of the question?
Thanks :smile:

Presume you realize that the 1-2(0.01) = 0.98 and that the cubic and higher order terms will be almost zero as x is small. So the approximation just refers to using up to the quadratic terms in the binomial expansion. So it should be simply subbing that value into the quadratic expression from the first part.

Reply 2

lau321

OP

10

Original post by mqb2766

Presume you realize that the 1-2(0.01) = 0.98 and that the cubic and higher order terms will be almost zero as x is small. So the approximation just refers to using up to the quadratic terms in the binomial expansion. So it should be simply subbing that value into the quadratic expression from the first part.