Question

Estimate sqrt(99.8) using differentials (or equivalently, a linear approximation).

Answer 1

Do you have a function we can use for a linear approximation?

Answer 2

this is the entire question
i'm not sure how to even start it

Answer 3

Okay wait.

Answer 4

Since it's a square root I assume f(x)= sqrt(x)

Answer 5

Did you get that?

Answer 6

ok

Answer 7

Now take the derivative of sqrt(x) .

Answer 8

1/2(x)^-1/2

Answer 9

Good!

Answer 10

The formula for a linearized function about a point x=a is :

\[L(x) = f(a)+f'(a)(x-a)\]

Answer 11

Since the question doesn't specify, we will assume the linearization occurs about x = 1.

Answer 12

Do you follow?

Answer 13

don't you think a= 100 is a better choice?

Answer 14

Meh. Okay 100.

Answer 15

I guess it's a better approximation.

Answer 16

i guess a=100

Answer 17

Now evaluate f(a) and f'(a)

Answer 18

f(100)=10
f'(100)=1/20

Answer 19

Good!

Answer 20

now plug it into that equation I gave you :) .

Answer 21

10+(1/20)(X-100)

Answer 22

Now plug in 99.8 :) .

Answer 23

9.99

Answer 24

Which is VERY close to the actual value :) . That's your answer :) .

Answer 25

thanks for the help

Answer 26

Welcome!