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

Question

Use a linear approximation (or differentials) to estimate the given number. square root of 100.8

Answer 1

STEP-1

F(x)= √x at x=a

We want to estimate f(100.8)= √100.8

L(x)= f(a)+ f'(a).(x-a)

Differentiate F(x) w.r.t x

d/dx([F(x)] = d/dx(√x)

F'(x)= 1/2√x

Take x=a and a=100

= 1/2√100

=1/20

STEP-2

L(x)= f(100) + f'(100) (x-100)

= √100 + 1/20 (x-20)

= 10 + x/20 -5

= 5+ x/20

√100.8 equivalent to L(100.8) = 5+100.8/20

= 5+ 5.04

= 10.04 ans