Question

HELP How do you find the limit of this?

Answer 1

\[\lim_{\theta \rightarrow 0}\frac{ \sin \theta }{ \theta + \tan \theta }\]

Answer 2

I figured I should replace tan theta with sin theta/cos theta

Answer 3

\[\lim_{\theta \rightarrow 0}\frac{ \sin \theta }{ \theta + \frac{ \sin \theta }{ \cos \theta } }\]

Answer 4

hmm

Answer 5

L'hospital shouldn't be allowed for his task though.

Answer 6

We haven't seen L'Hospital yet

Answer 7

I think I should get everything in terms of sinx or cosx

Answer 8

hmmm yeah... L'Hopital is pretty much for this case, a 0/0 case
BUT ..hmm decoupling it... doesn't seem to be lending so easy =(

Answer 9

@jdoe0001 lol why

Answer 10

well, as he/she said, they're not using L'Hopital yet

Answer 11

when u are in exam what u use ?

Answer 12

algebraic manipulations, of course.

Answer 13

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

Answer 14

@ChillOut @jdoe0001 look my other method

Answer 15

incorrect

Answer 16

lol really @mathmath333 show me my mistake

Answer 17

\(\lim_{x \rightarrow 0}\frac{ \sin(x) }{ x+\frac{ \sin(x) }{ \cos(x)} } = \lim_{x \rightarrow 0}\frac{ 1 }{\color{red}{ \frac{ x }{ \sin(x) }} +\frac{ 1 }{ \cos(x) }}=\lim_{x \rightarrow 0}\frac{ 1 }{ 0+1 }=1\)

Answer 18

lim x/sin(x) = 1, so the entire limit is 1/2

Answer 19

moreover the answer comming through L'hopital's rule is \(\dfrac{1}{2}\)

Answer 20

hmm i made mistake i know where is it

Answer 21

You almost got it right though

Answer 22

\[\lim_{x \rightarrow 0}\frac{ \sin(x) }{ x+\frac{ \sin(x) }{ \cos(x)} } = \lim_{x \rightarrow 0}\frac{ 1 }{ \frac{ x }{ \sin(x) } +\frac{ 1 }{ \cos(x) }}=\lim_{x \rightarrow 0}\frac{ 1 }{ 1+1 }=\frac{ 1 }{2 }\]

Answer 23

yup i made mistake @bts30 i know why u steal my solution lol

Answer 24

Noone's stealing. Don't worry if you want Little Stars!

Answer 25

xD

Answer 26

@mathmath333 @bts30 ty both for see my solution

Answer 27

@Fanduekisses u understand how i solve it

Answer 28

@dinamix Sorry I left.

Answer 29

@dinamix how did you get the 2nd part?

Answer 30

lim x-> 0 of 1/x/sinx + 1/cosx?

Answer 31

its just simplif sin(x) only

Answer 32

How did you get the denominator?

Answer 33

hmm i use sin(x)/sin(x) = 1 right ?

Answer 34

sinx/x

Answer 35

did u understand now how i get denominator

Answer 36

no :( how did you get x/sinx? where did the sinx come from? and how did you get 1/cosx? the denominator was originally x+ sinx/cosx how did it change?

Answer 37

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

Answer 38

yes

Answer 39

he divided both the upper and lower parts by sin(x). That's what he did.

Answer 40

:s

Answer 41

ty for @ChillOut explain