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
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

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.
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.

okay so just 1-10(0.01)+40(0.01)^2 ???(coefficients of expansion are 10 and 40, not just random numbers lol). Thanks!
Original post by lau321
okay so just 1-10(0.01)+40(0.01)^2 ???(coefficients of expansion are 10 and 40, not just random numbers lol). Thanks!

looks good.