Question

From the local linearizations of e^x and sinx near x=0, write down the local linearization of the function e^x sins

Answer 1

Near 0,

\(e^x \approx 1+x\)
\(\sin x \approx x\)

Answer 2

Is your function :

\(e^x \sin x\)

like this ?

Answer 3

yes

Answer 4

okay :) just multiply both the approximations and take only the linear terms :

\(e^x \sin x \approx (1+x)x\)

\(~~~~~~~~~~ \approx x + x^2\)

\(~~~~~~~~~~ \approx x \)

Answer 5

see if that makes more or less sense...

Answer 6

it does thanks!

Answer 7

np :)