Use a linear approximation (or differentiation) to estimate the given numbers.

a) (1.999)^4
b) cube root of 1001
c) 1/4.002

Need help! Even if you answer one of these that would be great.

linear approximation of a function f(x) at a point a is f(x) = f(a) +f(a) (x-a) where x is the point where you want to calculate
1)f(x) = x^4 a= 2 and x= 1.999
so 1.999^4 = 2^4 + 4*(2^3)*(- 0.001)= 15.968

2) f(x)=x^1/3 a= 1000 and x= 1001 so 1001^1/3= 10 +1 *1/3 * 1000^-2/3 = 10+1/300=10.0033


3) f(x)=1/x a= 4 x= 4.002 Now you can carry on

2^4
16

∛1000
10

1/4
=>.25