## v.s 2 years ago Find the limit. lim 3 − 3 tan x/sin x − cos x x→π/4

1. zordoloom

Could you write out how this looks. the division sign doesn't really indicate where the equation is divided.

2. zordoloom

At least put parenthesis where they belong.

3. v.s

lim (3 − 3 tan x)/(sin x − cos x) x→π/4

4. frx

First try to just put in the value pi/4 and decide if the function is defined in that point

5. zordoloom

you'll get -3sqrt(2)

6. frx

You see that sin pi/4- cos pi/4 equals zero so the function is undefined at pi/4 so what you want to do is to simplify the function

7. v.s

okaaaaaaaaay thambi

8. v.s

how do i simplify this?

9. chrisplusian

you can turn your denominator into$(3-3(\frac{ cosx }{ sinx })$ then split the numerator into two different fractions$\frac{ 3 }{ sinx-cosx } - \frac{ \frac{ sinx }{ cosx } }{ sinx-cosx }$

10. chrisplusian

sorry meant numerator

11. chrisplusian

and that should have been three times sine over cosine sorry I am messing it up pretty bad

12. v.s

loll itss okayy

13. v.s

i dont get the question

14. Coolsector

$\frac{ 3-3\tan(x) }{ \sin(x) - \cos(x) } \times \frac{ \sin(x) +\cos(x) }{ \sin(x) +\cos(x) }$

15. Coolsector

$\frac{ 3\sin(x) - 3\frac{ \sin^2(x) }{ \cos(x) } + 3\cos(x) -3\sin(x) }{ \sin^2(x) -\cos^2(x) }$

16. Coolsector

$\frac{ - 3\frac{ \sin^2(x) }{ \cos(x) } + 3\cos(x) }{ \sin^2(x) -\cos^2(x) }$

17. Coolsector

$\frac{ - 3\sin^2(x) + 3\cos^2(x) }{ \cos(x)[\sin^2(x) -\cos^2(x)] } = \frac{ -3 }{ \cos(x) }$

18. v.s

sorry i was busy

19. v.s

so i sub in pi/4

20. Coolsector

yes

21. v.s

-3/(1/sqroot2)

22. Coolsector

which simplifies into -3sqrt(2)

23. v.s

-sqroot2/3

24. Coolsector

no .. -3 * sqrt(2)

25. v.s

yeye

26. v.s

i gett it

27. Coolsector

$-3\sqrt2$

28. Coolsector

like this