1. Apr 20, 2010

### CR9

1. The problem statement, all variables and given/known data

Find limit as (r, θ)----> (0, pi/2) for the function:

r= (w secθ)/(secθ+tanθ)^(Vs/Vr)

Both w and Vs/Vr are constants in this question

3. The attempt at a solution

I tried with L'hopital but it didnt turn well as when I differentiate secθ, I got ln (secθ + tan θ)

which when θ approaches 0 still gives me infinite..

I've tried so long to get the answer, but nothing seems to work and I have to pass this up tommorow.

2. Apr 20, 2010

### tiny-tim

Hi CR9!

(have a pi: π )
(you mean "as θ----> π/2" ?)

Try multiplying top and bottom by cosθ

3. Apr 20, 2010

### CR9

Hi tiny Tim,

Thanks for the reply, yea I mean ( "as θ----> π/2" ?)

Multiplying cos top and bottom would cancel off the sec on top, but how do i times cos inside the denominator? It has power of Vs/Vr

Thanks

4. Apr 20, 2010

### tiny-tim

Hi CR9!

(secθ+tanθ)Vs/Vr = (secθ+tanθ)(secθ+tanθ)Vs/Vr - 1

5. Apr 20, 2010

### CR9

Hi Tiny Tim,

Thanks again for quick reply. You rock!

okay, so after multiplying cos top and bottom and expanding sec+ tan at the bottom as your previous post;

I got:

r/w=1/(1+sinθ )((secθ+tanθ)^(Vs/Vr-1) )

6. Apr 20, 2010

### CR9

But there are too many unknowns, how can I solve this in order to find a value for Vs/Vr.

I need to find the value for Vs/Vr and then find the angle.

7. Apr 20, 2010

### tiny-tim

Hi CR9!
or even 1/(1+sinθ)Vs/Vr(secθ)Vs/Vr - 1
no problemo … Vs/Vr is a constant, and θ -> π/2

(so, for example, the (1+sinθ) at the beginning obviously –> 2)

Deal with the three cases separately: Vs/Vr > = or < 1

8. Apr 20, 2010

### CR9

Hi Tiny Tim,
I was waiting for you online just now...

Anyway, Im still stuck at r/w=1/(1+sinθ )((secθ+tanθ)^(Vs/Vr-1)

What do i do from here?

9. Apr 20, 2010

### tiny-tim

Hi CR9!

I don't understand why you're stuck.

What does (1+sinθ ) tend to as θ -> π/2 ?

And what does (secθ+tanθ) tend to?

10. Apr 20, 2010

### CR9

as θ -> π/2,
(1+sin θ) approaches 2
(sec θ + tan θ) approaches infinite?

then from
r/w=1/(1+sinθ )((secθ+tanθ)^(Vs/Vr-1)

it will be
r/w= 1/(2)(infinite)^(vs/vr)-1

What do I do with this?

11. Apr 20, 2010

### tiny-tim

Well, what's ∞Vs/Vr-1 ?

12. Apr 20, 2010

### CR9

I dont know, Vs/vr could = 0 and it will become 1....

I dont have values for Vs/Vr, r and w...