Question

lim x -> 0 sin5x / 2x( 1+ 4 cos 2x ) . help !

Answer 1

\[\lim_{x \rightarrow 0}\frac{\sin5x*5}{5*2x(1+4\cos2x)}\]

Answer 2

and split down to (let lim sign aside) = \[\frac{sin5x}{5} * \frac{5}{2x(1+4cos2x)}\]

Answer 3

and lim of the first term =1 so, you just have limit of the second one =infinitive

Answer 4

hah ?
why math error ?

Answer 5

dont get

Answer 6

but i got 1/2 . i just want to make sure mine is right .

Answer 7

how to get 1/2?

Answer 8

you have the form 0/0, you must manipulate to avoid it.

Answer 9

or you can use l'Hopital rule. Either way is ok

Answer 10

huh ? never heard of it

Answer 11

ok, show me your work,

Answer 12

wait up

Answer 13

@Loser66 your process even ends up with 1/2. :)

Answer 14

sin5x /5x . 5x / 2x( 1 + 4 cos 2x ) . cut the x's at 5/2 . because sin5x/5x = 1

Answer 15

ah yes, I got it. thanks for pointing out my mistake,

Answer 16

then 1 x (5/ (2x0 ) ( 1 + 4 cos 2(0 )) = 1/2

Answer 17

@bellehunny I am sorry.!! I did it intuitively,

Answer 18

ohhh , no wonder

Answer 19

I didn't look up at my note , just remember something like that.... and made a dumb mistake

Answer 20

it's okay , everybody makes mistake . hehe

Answer 21

good, quite fair

Answer 22

btw , did i do it right ?