Question

Use a linear approximation (or differentials) to estimate the given number.

(1.999)^4

Answer 1

the formula for linear approximation is
L(x)=f(a)+F'(a)(x-a) here try a=2 since its very close to 1.999 therefore
L(x)=f(2)+F'(2)(x-2) since f(x)=x^4,f(2)=16,, f'(x)=4x^3, f'(2)=32
L(2)=16+32(2-2)=16 ANS

Answer 2

L(x)=16+32(x-2)
l(X)=16+32X-64
l(X)=32X-48 AT X=2
L(2)=16 ...ans

Answer 3

Oh, I see. So you find L(x) using the formula and then plugging in 1.999 into x and a.