Calculus Help Please
posted by Tenshi on .
Use a linear approximation (or differentials) to estimate the given number.
(1.999)^4

f(x) = f(a) + (xa) f'(a)
f(x) = x^4
df/dx = 4x^3
let a = 2
then f(a) = 2^4 = 16
f'(a) = 4*8 = 32
f(x) = 16 + (xa)(32)
xa =  .001
so
f(1.999) = 16 .001(32) = 16  .032
f(1.999) = 15.968
with calculator it is 15.968 also