Expert: Paul Klarreich - 5/5/2006

Question
Hi,
I asked you about the eight curve, you said that:
Vertical when y' is undefined, which means y = 0
I get the first bit. Why does it mean that y=0?
Don't you have to use the dy/dx (y') first and equate to something? I don't get how you arrived here.

Also, could you help me with another problem I'm stuck at?
Sorry it's messy.

S= N(the 's' integral sign with limits of the bottom is zero and the top one is infinity) [a(1-e^(-kt)]/k

where a,b and k are constants
Solve the improper integral to show that
S= Na/[b(b+k)]

Thanks very much
Emma

Answer
Hi, Emma,

You wrote:
I asked you about the eight curve, you said that:
Vertical when y' is undefined, which means y = 0
I get the first bit. Why does it mean that y=0?
Don't you have to use the dy/dx (y') first and equate to something? I don't get how you arrived here.

Also, could you help me with another problem I'm stuck at?
Sorry it's messy.

S= N(the 's' integral sign with limits of the bottom is zero and the top one is

infinity) [a(1-e^(-kt)]/k

where a,b and k are constants
Solve the improper integral to show that
S= Na/[b(b+k)]

Thanks very much
Emma
---------------------------
About the first question:

Vertical when y' is undefined, which means y = 0
I get the first bit. Why does it mean that y=0?

>> Sorry, I meant to say y' is undefined when the denominator, 2y, is zero.  And  2y = 0 means y = 0.

About the next:

Don't you have to use the dy/dx (y') first and equate to something?
>> Yes. Once we got our dy/dx, which, by the way, involved both x and y, which is typical of an IMP DIFF exercise, we first:

Equated it to zero.  That means the top = 0 for a fraction.
Equated it to infinity.  (Bad usage, I admit -- there is no such number as infinity.)  That means the bottom = 0 for a fraction.
------------------------------

For your other problem:

S= N(the 's' integral sign with limits of the bottom is zero and the top one is infinity) [a(1-e^(-kt)]/k

where a,b and k are constants
Solve the improper integral to show that
S= Na/[b(b+k)]

I will write it this way.  USE A FIXED-SIZE FONT TO VIEW THIS.

{t=inf a(1 - e^(-kt)     
N|      -------------
}t=0        k

Now some things seem to be missing or useless:

A. You don't need to waste effort on the N.
B. Where is the b?
C. You need a 'dt' in the integral.

Please fix and resend.