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  1. A

    Ellipse Property Proof:

    Can someone show me the proof for the following (a diagram would also be helpful). "A tangent at a point P on an ellipse is equally inclined to the focal chords through P." thanks in advance.
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    Proving ellipse property

    Show that the sum of the distances from any point P on the ellipse x^2/a^2 + y^2/b^2 = 1 to the two foci is equal to 2a.
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    Perms/Combs

    5 travellers arrive at a town that has 3 hotels. Two of the travellers, Joanne and David, wish to stay in the same hotel. In how many ways can the 5 travellers occupy the hotels, if each hotel must be occupied by at least 1 person?
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    Inverse functions

    Let y = x^3 - 3x^2 - 1 (for x >=2). Find the slope of the tangent to the inverse function at x = -1.
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    integration

    how would i integrate x*sqrt(1-4x)?
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    Using t-formulae in integration

    Using the substitution t = tan(x/2), evaluate the integral dx /(13 + 5sinx + 12cosx) from x=0 to x=pi/3.
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    integration using trig substitutions? :S

    Evaluate the integral x^2/sqrt(4-x^2) dx from x = -1 to x = sqrt3 using the substitution x = 2sin(theta).
  8. A

    integration...

    integrate (x^2-1)/(x^2+x-6)
  9. A

    integration by parts

    integrate x^2cosx dx from x = 0 to x = pi/2
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    integration

    integrate x/[(x^2+2)(x-3)]
  11. A

    Volumes!

    The base of a particular solid is x^2 + y^2 = 4. Find the volume of the solid if every cross-section perpendicular to the x-axis is a parabolic segment with axis of symmetry passing through the x-axis and height the length of its base. (answer = 256/9)
  12. A

    integration

    integrate x*sqrt(2x-x^2)
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    cylindrical shells

    when finding volumes using cylindrical shells, how do you determine the upper and lower limits for the integral? :S
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    Volumes - Slicing

    Use the method of slicing to find the volume of the solid obtained by rotating the region enclosed within the circle (x-1)^2 + y^2 = 1 about the y-axis.
  15. A

    integration by parts

    integrate (secx)^3
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    integral of sec(x) and integration by parts.

    What is the fastest/easiest way to integrate sec(x)? also, what is the integral of: xsecxtanx ?
  17. A

    integration by sub.

    find the integral of x^3/sqrt(x^2+1)
  18. A

    Integration.

    Find the area bounded by the curve y = e^x/(1+e^2x), the x-axis, the y-axis and the ordinate x = 1/2ln3.
  19. A

    Advantages of globalisation?

    What are the benefits/advantages of globalisation? :)
  20. A

    oxidising agents!?

    Which of the following species is the strongest oxidising agent? a) Cu2+ b) Al3+ c) Fe3+ d) Ca2+ Can someone please give me an in-depth explanation on how what the answer is and why? :S
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