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Original Question
Use a linear approximation (or differentials) to estimate the given number. e^-0.01Asked by Tenshi
Use a linear approximation (or differentials) to estimate the given number.
(1.999)^4
(1.999)^4
Answers
Answered by
Damon
f(x) = f(a) + (x-a) 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 + (x-a)(32)
x-a = - .001
so
f(1.999) = 16 -.001(32) = 16 - .032
f(1.999) = 15.968
with calculator it is 15.968 also
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 + (x-a)(32)
x-a = - .001
so
f(1.999) = 16 -.001(32) = 16 - .032
f(1.999) = 15.968
with calculator it is 15.968 also
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