Question

What is the limit as x->0 of sin5x/sin4x?

Answer 1

5/4

Answer 2

Wait it isnt 4/5? thats what i was thinking

Answer 3

nope its 5/4

Answer 4

Alright. any idea why?I try it and get 4/5?

Answer 5

\[\lim_{x \rightarrow 0}\frac{\sin(Ax)}{\sin(Bx)}=\lim_{x \rightarrow 0}\frac{A}{B} \cdot \frac{Bx}{Ax} \cdot \frac{\sin(Ax)}{\sin(Bx)}\]
\[=\lim_{x \rightarrow 0}\frac{A}{B}\frac{\sin(Ax)}{Ax} \cdot \frac{Bx}{\sin(Bx)}=\frac{A}{B} \cdot 1 \cdot 1 \]

Answer 6

ah i think i see it. Thanks myininaya for the explaination

Answer 7

np
so this case i provided you is a general one

Answer 8

you understand it?

Answer 9

yes I think so. It would be 5/4 because its just 5/4 multipled by 1 twice?

Answer 10

MAybe I dont get it. Not sure how you get to the first part then the 2nd.

Answer 11

yes A=5
B=4

Answer 12

i just multiplied by 1

Answer 13

\[1=\frac{ABx}{ABx}\]

Answer 14

then i rearrange so i could write sin(Ax)/Ax and Bx/sin(Bx)

Answer 15

and then i had A/B left

Answer 16

why did you multiple by A/B and Bx/Ax?

Answer 17

i know sin(Ax)/Ax->1 as x->0
i know Bx/sin(Bx)->1 as x->0

so i was thinking how do i get this Bx/Ax
i have to also multiply by A/B

Answer 18

Yeah I dont see it at all really..Where did you get the first part from and how did that equal the second part?I dont see how it just suddenly equals sin(ax)/ax

Answer 19

\[\frac{ABx}{ABx} \cdot \frac{\sin(Ax)}{\sin(Bx)}=\frac{A}{B} \cdot \frac{Bx}{Ax} \cdot \frac{\sin(Ax)}{\sin(Bx)}\]
\[=\frac{A}{B} \cdot \frac{\sin(Ax)}{Ax} \cdot \frac{Bx}{\sin(Bx)}\]

Answer 20

so you don't understand this?

Answer 21

i just moved stuff around

Answer 22

remember multiplication is commutative

Answer 23

Yeah I'm not seeing it... I dont get how Sin5x/sin4x = (5/4)sinx5x/5x)(4x/sin4x)

Answer 24

It just looks like there is way too much there

Answer 25

\[\frac{\sin(5x)}{\sin(4x)}=\frac{5(4)x}{5(4)x} \cdot \frac{\sin(5x)}{\sin(4x)}=\frac{\sin(5x)}{5x} \cdot \frac{4x}{\sin(4x)} \cdot \frac{5}{4}=1(1)(5/4)=5/4\]

Answer 26

and thats of course if x->0 then L=5/4

Answer 27

i don't understand what part you aren't understanding

Answer 28

Oh I guess

Answer 29

its just rearranging

Answer 30

a(b)=b(a)

Answer 31

you know this right?

Answer 32

example:
2(4)=4(2)

Answer 33

what does sin(x)/x go to as x goes to 0?

Answer 34

Yes I guess it now. Just havent really done rearranging with fractions like that. Wasnt sure if we could

Answer 35

Yes I guess it now. Just havent really done rearranging with fractions like that. Wasnt sure if we could

Answer 36

\[\lim_{u(x) \rightarrow 0}\frac{\sin(u(x))}{u(x)}=1\]

Answer 37

right?