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Thread: Calc II midterm review guide

  1. #1
    Aug 2009

    Calc II midterm review guide

    So here is the story. I offered to help a friend with a few problems that he did not understand so he dropped off the practice test and I was gonna do the problems and then explain to him how i solved them, the only problem is that i am lost on three problems, I took calc II at a community college and apperently we skipped a couple important sections. Thanks in advance.

    I believe this is a dot product problem, but like i said i think my teacher skipped this.

    a=<-4,0,3> b=<1,-2,2>


    B.)3a + b

    C.)a . b

    D.) the angle between a and b

    E.) a X b

    F.) comp (sub b) a

    Given the point P(2,-2,0) and the line l with parametric equations x=2t, y=1-t z=3+t find the following.

    A.) Parametric and symmetric equations of the line through P and parallel to the line l.

    B.) an equation of the plane containing P and perpendicular to l

    C.) the point of intersection of the given line l with the plane 2x-3y+z-4=0

    and if you could set up this integral and i will evaluate it that would be a huge help.

    Polar curves r=4cos2theta and r=2
    1.)the integral for the area inside r=4cos2theta and outside r=2

    2.)and the integral for the area common to both.

    Thanks in advance i have one more question but ive actually resorted to facebooking my old calc teacher from high school to help me out. I feel bad asking for help but I am so lost and never learned this or seem to have forgotten it. If at all possible id like to have these done by sunday so i can explain it to him sunday night so on monday he can take his exam with all the info needed.
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  2. #2
    Member eXist's Avatar
    Aug 2009
    A) |a| = magnitude = length of the vector.
    To find the magnitude use the formula:  l = \sqrt{x_1^2 + x_2^2 + ... + x_n^2} where n is the number of coordinates you have (in this case 3).

    B) Fairly simple: 3a + b = 3<-4, 0 , 3> + <1, -2, 2> = <-12, 0, 9> + <1, -2, 2> Scalars distribute through vectors like they do through parenthesis, then you just add the corresponding coordinates.

    C) This is called the dot product: a \cdot b = (a_1 * b_1) + (a_2 * b_2) + ... + (a_n * b_n) n being the number of coordinates you have, in this case 3 again. The result of the dot product should always be a scalar.

    D) The formula:  cos \theta = \frac{a\cdot b}{|a||b|} can be used where \theta is the angle between the vectors.

    E) This is known as the cross product. It is only defined (that I know off) in three dimensional space R^3. Check out Cross product - Wikipedia, the free encyclopedia and look under computing the cross prodcut. They explain it better than I can.

    F) Is there more information about this one? I myself am not exactly sure what is defined by comp() or sub(). Maybe compliment? Not sure.

    And this looks like Calc 3 by the way, but maybe his Calc 2 overlaps into Calc 3? Not sure .
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