Simple Calc Linear Approximation

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

Sin 1(degree)

1 / 4.002

square root of 99.8


Alright, I don't really know where exactly to start on this. If you can answer at least 1 of these answers with steps and then give me the answers to the other 2 I think I could figure it out by myself. But I'd prefer if you gave the answer to all 3 with steps please. Thanks.

Only one question at a time.

I will do the last one

let f(x) = √x

at x = 100
f(100) = 10

f ' (x) = (1/2)(1/√x)
f ' (100) = (1/2)1/10) = 1/20

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

L(x) = 10 + (1/20)(x - 100)

L(x) = 10 + (x/20) - 5
L(x) = (x/20) + 5

√99.8 = L(99.8) = (99.8/20) + 5

= 9.99