An approximate value for 0.8^1/2 is found by substituting x=0.1 into the first three terms of the binomial expansion for (1−2x)^1/2 The percentage error in this approximate value is ____ % (3 d.p.) ?

1 Answer
Jul 23, 2018

The error is #=0.112%#

Explanation:

The Taylor's expansion is

#(1-2x)^(1/2)=1-x-x^2/2#

#x=0.1#

#(1-2xx0.1)^(1/2)=(0.8)^(1/2)#

#=1-0.1-(0.1)^2/2#

#=0.9-0.005#

#=0.895#

The value of

#sqrt(0.8)=0.894#

The percentage error is

#=(|0.894-0.895|)/0.894*100#

#=0.001/0.894*100#

#=0.112%#