Question

how to find the limit of the f(x) sin(2x)/4x as it approaches 0 without a calculator

Answer 1

ok well, do you know the limit of sinx/x as it approaches 0?

Answer 2

1

Answer 3

you will need to use a trig identity

Answer 4

oh nevermind no you won't. you just have to plug in 0

Answer 5

right, so you have 2x instead of x, you want to get a 2x on the bottom, how would you do that with 4x?

Answer 6

plugging in 0 would get you 0/0 which is no bueno

Answer 7

ok so then yes you will need an identity

Answer 8

you want to get 2x on the bottom, so you would have to divide by 2

Answer 9

and you can take \[\frac{ 1 }{ 4 }\] as a constant

Answer 10

right, you would factor out a 2

Answer 11

you could take 1/4 out as a constant, but then you'd still have sin(2x)/x in your limit. Then you would need to multiple in 2/2 to get 2sin(2x)/2x

Answer 12

\[\lim_{x \rightarrow 0}\frac{ \sin(2x) }{ 2x} * \frac{ 1 }{ 2 }\]

Answer 13

then you can use your limit identity, but you'd get the same answer.

Answer 14

yes!

Answer 15

now, what's the \[\lim_{x \rightarrow 0}\frac{ \sin(2x) }{ 2x }\]

Answer 16

1 still, right?

Answer 17

yep

Answer 18

all you're left with is 1/2 and that's your answer. :)

Answer 19

thank you so much!!!

Answer 20

No worries. :)