Question

limit problem

Answer 1

last one i need help on (: @aegidious

Answer 2

Already here :)

Answer 3

oooooooh okay, this one is going to deal with trigonometric identities. Do you remember how we stretched out the numerator of the last equation with what it equaled? Well we're going to do the same thing here with trigonometric identities that equal sine so we can stretch out the denominator into something else

Answer 4

ohhhh

Answer 5

mmmmhmmm aren't trig identities fun? -_- *sarcasm* lol

Answer 6

okay ummm how to start...

Answer 7

hahaha oh yeahhh

Answer 8

i did it before and got 2/5 and i was going by my textbook but i dont think its right

Answer 9

well you understand that

tan(x) = sin(x) / cos(x) right?

then that must also mean that

sin(x) = cos(x)*tan(x)

Answer 10

yess

Answer 11

hmmm....

Answer 12

trig problems make me nervous.... give me a minute to think...

Answer 13

hahaha okay

Answer 14

hmmmm does your textbook give you 2/5? or was that what you got?

Answer 15

thats what i got

Answer 16

it could be totally wrong

Answer 17

okay, now say we have used trig identities to get

tan(-2x)*cos(-2x)
---------------
tan(-5x)*cos(-5x)

we need to use trig identities to get the tan out of it. 2/5 would be right if the tan wasn't there, but it's just making the whole thing complicated -_- so hmmmm

Answer 18

and you can't simply factor the tangents out, because the x's are being multiplied by two different constants...

Answer 19

oh this is really hard hahah

Answer 20

mmmmhmmmmm tell me about it...

Answer 21

ughhh nobody wants to help

Answer 22

i put it into wolfram and got 2/5 (:

Answer 23

Using the fact that sine is an odd function, we can reduce this (somewhat) to
\[\frac{\sin(-2x)}{\sin(-5x)}=\frac{-\sin2x}{-\sin5x}=\frac{\sin2x}{\sin5x}\]
Now try rewriting the expression so that you can make use of the known limits,
\[\lim_{x\to0}\frac{\sin ax}{ax}=\lim_{x\to0}\frac{ax}{\sin ax}=1\]
for \(a\not=0\).

Answer 24

you got 1? @SithsAndGiggles

Answer 25

@jim_thompson5910 what do you get?

Answer 26

I said no such thing. I'm giving you hints to get the right answer, which is indeed 2/5.

Answer 27

are you allowed to use L'Hospital's Rule?