Question

Finding formula for differential dy and linear approximations, please check my work.

Answer 1

It's a little dark, sorry!

Answer 2

There's one more part which I will upload in just a moment :)

Answer 3

Ah, now I see the boo boo.

Answer 4

f'(5)= woops, you dropped the 3 that was in the back

Answer 5

ah!

Answer 6

Besides that, looks good :)
You can see that this `red line` approximates your curve very well around x=5.
https://www.desmos.com/calculator/ttlbwonl4o

Answer 7

so it would be 3/32

Answer 8

Ya, the f'(5) is the only thing that should change, instead of 1/32 you get 3/32 because of that 3 we lost earlier.

Answer 9

Part c.. hmm

Answer 10

em yeah so the formula changes and the answer to part c changes

Answer 11

Oh good call :)

Answer 12

to 1.999 lol

Answer 13

wait huh

Answer 14

that is the same answer o.o

Answer 15

oh some of the decimal numbers change.

Answer 16

well the ....ten thousands place will have changed :)
instead of 1.9997 you should get 1.99906 or something like that, ya?

Answer 17

yyep yep
so i guess I can write 1.9991

Answer 18

does it all look good now? :)

Answer 19

Oh wait, mine is giving me another 9...
1.99990625
lemme make sure I didn't mess something up..

Answer 20

2+(3/32)(4.99-5)

Answer 21

\[\large\rm f(4.99)\approx f(5)+f'(5)(4.99-5)\]\[\large\rm f(4.99)\approx 2+\frac{3}{32}(-0.001)\]

Answer 22

Ya looks good ^^

Answer 23

-0.01* hehe my bad :)

Answer 24

Excellent! thank you.