Answer
a)0.41
b)0.4
c)0.01
Work Step by Step
a) we need to find change which is f(x0+dx)-f(x0).
f(x)= x^2+2x x0=1 dx=0.1
f(1+0.1)-f(1)= (1.1^2+2*1.1)- (1^2+2*1)= 0.41
b) value of estimate equals to derirative of f
df= f'(x0)dx
df= (2x+2)dx at x0=1
df= 4* 0.1 =0.4 answer 0.4
c) approximation error is (the change - value of estimate)
Change in f -df
Change in f = 0.41 (look a variant)
df= 0.4 (look b variant)
So 0.41-0.4 = 0.01
0.01 is error.
