Question

Use Series to evaluate to 3 decimals

Answer 1

\[\int\limits_{0}^{0.1}\frac{ Sin x }{ x } dx\]

Answer 2

replace sin(x) with its series representation and integrate each piece until the number stpos changing above the 4th decimal... then round to 3 decimals.

Answer 3

thanks :D

Answer 4

make sense?

Answer 5

\[\sin x=x - \frac{ x^3 }{ 3! }+\frac{ x^5 }{ 5! }-\frac{ x^7 }{ 7! } \pm \cdots\]

Answer 6

yes thanks it help me a lot :D

Answer 7

awesome!

Answer 8

one more sir can you help me with this

Answer 9

i'll do my best

Answer 10

\[\int\limits_{0}^{0.1}e ^{-x ^{2}}dx\]

Answer 11

is this same with the series of e^x?

Answer 12

yes, just replace x with -x^2

\[e^x = 1+x+\frac{ x^2 }{ 2! }+\frac{ x^3 }{ 3! }+\frac{ x^4 }{ 4! }+\cdots\]

Answer 13

yes i got it right thanks big help sir :D

Answer 14

you're so welcome!