Question

"Use a linear approximation to estimate the given number"

e^(0.1)

Linear approximation: L(x)=f(a)-f'(a)(x-a)

Answer 1

\[e^{0.1}\]function \(e^{x}\); what would I set as \(a\)?

Answer 2

I guess do it like \[\large y = e^x \]\[\large \frac{ dy }{ dx } = e^x\]\[\large \Delta y = e^x \Delta x \]then you could use e^0 as your known value, then for e^0.1 Delta x would be 0.1\[\large e^{0.1} = e^0 + \Delta y\]

Answer 3

I think they want me to use the L(x) which I added into the original post.
Sorry about that

Answer 4

Yeah that's the same thing as what i gave, just with things plugged in.

Answer 5

\[\large L(x)=f(a)-f'(a)(x-a) \]\[\large L(0.1)=e^0-e^0(0.1-0) \]

Answer 6

So \(a=0\)?

Answer 7

Yes

Answer 8

Oh, alright. Gotcha.

Answer 9

@kittiwitti1 Do you understand why @agent0smith 's formula is exactly the same thing as yours?

Answer 10

Whoops, forgot to close this question.