# caseclosed

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63

1. ## Differential Equation Model help please

This is from the book, need help changing it into mathematical model. "Consider a tank used for certain hydrodynamic experiments. After one experiment the tank contains 200 litres of a dye solution with a concentration of 1 g/litre. To prepare for the next experiment, the tank is rinsed with fresh water flowing in at a rate of 2 litres/min, the well-stirred solution flowing out at the same rate. Find the time that will elapse before the concentration of dye in the tank readches 1% of its original value."
2. ## Argument(Angle from dot product)

ok, I have claried this, apprarently it was for angle between 2 planes... grr those conventional ways
3. ## Calculus Fun Challenge

$\int{\sec{x}^3dx}=F$ $u=Sec(x)$ $du=Sec(x)Tan(x)dx$ $dv=Sec(x)^2dx$ $v=Tan(x)$ $F=$$Sec(x)Tan(x)$ $\int{\tan{x}^2sec{x}dx}$ $F=$$Tan(x)^2=Sec(x)^2-1$ $F=$$Sec(x)Tan(x)$ $-\int{\sec{x}^3dx}$$+\int{sec{x}dx}$ $F=$$Sec(x)Tan(x)$ $-F$$+ln(sec(x)+tan(x))$ $2F=$$Sec(x)Tan(x)$ $+ln(sec(x)+tan(x))$ $F=$$(Sec(x)Tan(x))/2$ $+(ln(sec(x)+tan(x))/2$ thank you very much for giving me the hint. I so forgot how to do this.
4. ## Argument(Angle from dot product)

well, I just did the questions in the book and my professor's method doesn't match the answer in the book. He says the book is wrong...... the book is Thomas's Calculus 11th edition. also I see nowhere online where it says absolute value of dot product.
5. ## Argument(Angle from dot product)

cos(theta)= (A.B)/(lAllBl) OR cos(theta)=(lA.Bl)/(lAllBl) ---->my teacher insist this one is right and other one is wrong
6. ## integration help

ok, that's why... I should just leave it as sec^3 instead of changing using trig indentity. thank you very much.
7. ## integration help

yes, I tried setting u=(x^2+1)^(1/2) and dv=dx but I am not getting any log in the answer which means wrong. using the parts on sec(theta)^3 gets me nowhere, I change to (tan(x)^2+1)sec(x) and then set u=tan(x)^2 and dv=sec(x) dx which lead me to very complicated. I know I did this before but I don't remember how I did it.
8. ## integration help

integrate (1+x^2)^(1/2) I used trig substitution and gotten integrate sec(theta)^3 but no clue what to do ....
9. ## vectors and the geometry of space

find the point of intersection of the lines x=2t+1, y=3t+2, z=4t+3, and x=s+2, y=2s+4, z=-4s-1, and the find the plane determined by these lines. I don't know what to do...
10. ## Help needed on complicated differentiation and integration

oh, because it looks like the Calculus 2 stuff I did this year, thats why I was wondering.
11. ## Help needed on complicated differentiation and integration

so what grade are you in since you are doing this?
12. ## differentiation question

AH!!!! thanks, why didn't that hit me, heh
13. ## differentiation question

how to differentiate sin(x)^x for 0<x<pi/2
14. ## integration question

ok, now I understand it, basically constant can be thrown out.
15. ## integration question

I see, I hope the exam does not give mathematica answer as the chice because I have absolutely no clue how to get sec(x)^2/2, anyone know how to get that?
16. ## integration question

This integral Tan(x)^3+Tan(x) doing it by hang gives Tan(x)^2/2 Mathematica gives Sec(x)^2/2 so why the difference, are both correct, how to get the mathematica answer by hand?
17. ## sequence monotone increasing or decreasing

I learned to use this way instead of the others an+1/an so when the ratio get smaller and smaller for n>1 does that mean it is decreasing? and not increasing nor decreasing when the ratio stay same for all n>1 like (x^2+2x)/(x^2+2x+2).
18. ## upper and lower bound of the sequence

so basically, if there is an upper and lower bound for this type of sequence, it is either a1 and where it converges?
19. ## limits.... gahh either I forgot or just no clue

heh, I just found out what I forgot, I forgot to balance out the e by adding natural log. so it would be e^L=e^(ln(e^x+x)*(1/x)) and then by using properties of log and change L to quotient to get (e^x+x)/x so that it is form infinity/infinity and now using L Hopital's rule to get (1+1)/1 so it is 2 but 2=L so the answer would be e^2. woot...
20. ## limits.... gahh either I forgot or just no clue

limit of (e^x+x)^(1/x) as x approaches 0 I remember using e^L where L=(e^x+x)^(1/x) for this 1^infinity form what do I do now?
21. ## upper and lower bound of the sequence

I got (2)/(n!(n+2)) so as n increases to infinity, the thing approaches 0 so that is why it is decreasing right? and less than 1 means it converges. but I don't understand where the upper/lower bound, what is it.... suppose to be a finite number? or is it like lower bound 0 since it is approaching 0 and upper bound unbounded?
22. ## upper and lower bound of the sequence

how do I find the upper and lower bound of this sequence? (2^(n-1))/(n+1)!
23. ## Mega hard integral part 3 <plz help>

awww, I did parts twice that is why did not work for me.
24. ## question on partial fraction decomposition

thank you, I didn't see how the numerator is bigger than the denominator, so when the largest power is same on top and bottom, long division is neccesary? This one looked like a proper fraction to me
25. ## question on partial fraction decomposition

woops, I typed it wrong here I meant $\frac{x^3+2}{x^3-x}$ so why is there extra +1 for mathematica and calculator? when I do it I get $\frac{A}{X} + \frac{B}{X-1} + \frac{C}{X+1}$ that is how I got my 3 terms.
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