iamdan08's spec questions

[Mao]

I have another question:

A spherical balloon is inflated by blowing of air into it every 5 seconds. What is the rate of change of the volume of the balloon (in ), at the moment when the radius is 5cm?

Is it just /s???

Thanks 

you are right, the rate of change of volume has not changed.

though I think the question is trying to ask for the rate of change of radius, which you would use related rates to solve.

, the question did not specify the rate of change of radius.

[iamdan08]

A couple more questions:

Find the oblique asymptote of

and:

Find an antiderivative for

[Damo17]

A couple more questions:

Find the oblique asymptote of

expand and simplify to get:


so:



so the oblique asymptote is:

[Mao]

Let

(negative solution discarded as )



the rest is trivial

[iamdan08]

Thanks! Another question:

Evaluate the following integrals:





 

[kamil9876]

u want only a power of 2 on the sec. since .

You do this by using the identity that relates them.

second one is actually easier:



substituion of does the trick.

For the other one its a similair idea, but use to get rid of one of the powers on the sec.

[Mao]

[iamdan08]

Awesome...Thanks guys!

[iamdan08]

2 more questions:

Solve the initial value problem

and

and also:

Find the volume of the solid generated by rotating the region between the curves and about the x-axis

Thank you...

 

[kamil9876]

anti-differentiate both sides with respect to dx and you will get a nice surprise

[d0minicz]

wats the answer for the solid revolution one?

[kamil9876]

 

you can easily see that this is an increasing parabola and so if you draw a graph you can see that it intercepts the line y=x at two points above the y axis and the line y=x is above the parabola.

find intercepts:

x^2-4x+4=x
x^2-5x+4=0
(x-4)(x-1)=0

Hence x=4 and x=1 are your terminals:

and i fogot how to put terminals in latex.

[iamdan08]

Oh ok! Awesome. Thanks for that kamil9876!!

[dekoyl]

and i fogot how to put terminals in latex.

Offtopic:
To put terminals in LaTeX:

Code: [Select]

V=\int_{1}^{4}x-x^2-4x+4.dx will give

[iamdan08]

Another question:

The number of bacteria in a culture can be modeled according to the equation

After 3 hours the culture is washed with a solution harmful to the bacteria, and the bacteria are killed off at a rate of 4500 per hour.

Find the number of bacteria in the culture for any time t>3.


I'm not to sure what i'm supposed to do...

Thanks