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I am in calculus 3 and the chapter on vectors (cross product) one of the properties is:
u x v = 0 if and only if u + v are scalar multiples of each other
I need to prove u x v = 0
A hint we have is:
u x v = 0
assume -> deriv ; and then take it back the other way.
1)Find equation of ellipse
foci:(0,+-5)
major axis length=14
-that give me that so I have deter that I can use the vertical major axis which is (x-h)^2/b^2 + (y-k)^2/a^2=1
-i deter my center (0,0) and a=7
How do I find what b= so I can make the equation?
2)Eliminate the perameter and write corresponding reactangular equation
x=sec thetha , y=tan theta
I don't know where to start.
3)Find all points(if any) of horiz and vert. tangency to curve
x=4cos^2 theta , y=2sin theta
- for y i got the points (0,2),(0,-2)
- i cant seem to find anything for x=
-i got the deriv to be -8*sintheta*costheta
and that =0 at 0,pi/2,pi,3pi/2 so what does that mean?
4) convert the rectangular equation to polar form
(x^2+y^2)^2-9(x^2-y^2)=0
- i got about half way and am now stuck
Any help on ANY of these would be appreciated. Thanks
A fair coin is tossed repeatedly. The probability that the first head occurs on the nth toss is P(n)=(1/2)^n. When this action is repeated many times, the average # of tosses required until the first head is:
E(n)=sum from 1 to inf n*P(n)
This # is called the expected value of n
A) use the power series: 1/1-x = sum from 0 to inf of x^n, for |x|<1 to get a power series representation for f(x)=1/(1-x)^2 and give interval of convergence
B) what is the relation between E(n) and the series found in (a)?
C) what is the expected value of n? Be sure to give specific reason why you can make your conclusion.
I am completely clueless on this. If someone could just help me on each part not exactly answer it that would be very helpful. Thanks
Find Power Series and determine the Interval of Convergence
g(x)=3x/(x^2+x-2) , c=0
- after doing partial fractions and getting the form into a/1-r and finding endpoints, then combining both and I got the Interval of Convergence to be (-1,1) is that right?
f(x)=1/2-x ,c=5
- I tried this 1 way but the book did it another way and got a diff. answer so can someone work this ?
Use the Power Series 1/1+x = E (-1)^n*x^n to determine a power series , c=0. Identify Interval of Converg.
f(x)=1/(x+1)^2 = d/dx [1/x+1]
- I dont get how to do this
f(x)=ln(x+1) = S 1/x+1 dx
- this one either
I had a test today and these were some of the problems on there and I was just wanting to check and see if I got them right.
Deter. Converge or Diverge
sum from 0(i think) to inf of 1/(4x^2+(or - forgot) 1)
I got p=2 so its converge
sum from 1 to inf of n*e^x(^2)
I got (e^-1)/2 so it converges
sum from 1 to inf of (3/10)^n
r=3/10 so converges
sum from 1 to inf of 1/(n^9/7)+1)
p=9/7 so converge
Deter if converge or diverge and if converge find sum using partial frac.
sum from 1(i think) to inf of 2/(x^2-1)
I got converges and sum is 2
Deter if converges absolutely, conditionally, or diverges
sum from 1 to inf of (-1)^n/(x+(i think)1)
I got the E (absolute value)A_n = 1 because I compared 1/(x+1) with 1/x and got 1 so converges conditionally?
I have a test tomorrow and got some quick questions on some problems. I don't really need them worked out I just need help starting them. Thanks
Determine whether the series is convergent or divergent.
seriesSum((5-2 sqrt(x))/x^3, n, 1, infinity)
* Do I use p-series here and do I do limit comparison test?
seriesSum(1/(n ln(n)^2), n, 2, infinity)
* same question as above with p-series.
seriesSum((n+2)/(n+1)^3, n, 3, infinity)
*same as above also.
seriesSum((n+5)/root(n^7+n^2, 3), n, 1, infinity)
* p-series and how would I go about determining?...what can I use?
seriesSum(1/e^n+1/(n (n+1)), n, 1, infinity)
* I don't know where to start on this one. And find sum.
How do I get it to show the equation instead of just the wording? That would make it look a whole lot better.
For example
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit.
How do you determine convergence or divergence?
An=( ln sqrt(n) ) / n
An=( n^2/(2n+1)) - (n^2/(2n-1))
Find the sum of the convergent series. ( I got some of these worked but they got tough )
Sum from 1 to inf = 1 / ((2n+1)(2n+3))
sum from 0 to inf = 2 (-2/3)^n
And that is just to name a few.:o
I just started Calc 3 in summer school and our teacher was not here (monday) the first day of class when we got some notes on ch 9.1 Sequences.....Determining Convergence or Divergence, Squeeze Theoremand determining if it is bounded. (Going by Calculus Eight Edition by Larson,Hostetler, Edwards). Today we moved on to 9.2 which has to deal with Series and Convergence....which i need more help on 9.1 than this.... and a few theorems. I am completely lost right now and have just a slight clue what is going on. The teacher is not all that clear and just puts it on the board and really doesn't explain it. I was wondering if there was a site or someone could explain these 2 sections to me. I have tried reading the book but that hasn't helped much.
Calculus 2 help?
Need help with these questions. I have a test tomorrow and need help on knowing how to work these.....S stands for integration. And just help on any of these would be fine. Thanks
1) S 2/(x-9)^2 dx .... i got the answer -2/(x-9) but how did they get that because as far as I got is 2S1/(u^2) dx
2) S [x + 1/(3x-1)^3] dx
3) S (x^2-3)/(-x^3+9x+1) dx ......long division?
4) cotx ln(sinx) dx ........ havn't tried to work it yet.
5) S 2/((2x-1)^2+4) dx ...here you use arctan formula which is du/a^2+u^2 = 1/a arctan(u/a)+c and I have kinda got a and u figured out just need help putting in because this is diff. from what we did in class.
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