Question

By using the fact that lim x->0 (sinx/x) = 1,or otherwise
find lim x->0 (2x^3+4x)/(sin2x)

PLEASE HELP

Answer 1

So you don't get to use l'Hospital's rule?

Answer 2

No I don't.

Answer 3

Could you please assist me? The help would be very much appreciated.

Answer 4

\[
\sin(2x) = 2\sin(x)\cos(x)
\]

Answer 5

\[
2x^3+4x =2x(x^3+2)
\]

Answer 6

then just factor out the \(\sin(x)\) and \(x\)

Answer 7

Since \[
\lim f(x)g(x) = [\lim f(x)][\lim g(x)]
\]

Answer 8

do you get it?

Answer 9

it would be x/sinx * (x^3+2)/cosx?

Answer 10

Yeah

Answer 11

so the answer is 2?

Answer 12

yeah
http://www.wolframalpha.com/input/?i=lim+x-%3E0+(2x%5E3%2B4x)%2F(sin2x)

Answer 13

Oh thank you, wow how do I like "pay" you on this site?

Answer 14

Become a fan?