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I tried, but i can't get it.

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.

but why not make the absolute value of (ex - a) = ex - a, instad of a - ex?

ah is that short method allowed? Because the method using distance formula is long and confusing at the end. why is the absolute of (ex - a) = a - ex?

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.

Thong wishes he had Fiona ;) (But yea an explanation of how to do the question would be helpful)

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?

is there a simpler way of doing this? I simply differentiated the the original equation, found the reciprocal (i.e. dx/dy) and then subbed in x = -1 and i got the same answer (1/9). Or is that method incorrect?

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

how would i integrate x*sqrt(1-4x)?

i got.. x - 8/5ln(x+3) + 3/5ln(x-2) + C... Is that right?

thanks :)

i've attempted all the questions i've posted several times. But i keep getting the same answers (which are different to the answers in the textbook.) So i normally just post them up here to double check. Normally it turns out that the textbook is in fact wrong. :( (BTW I'm using the Phoenix...

Using the substitution t = tan(x/2), evaluate the integral dx /(13 + 5sinx + 12cosx) from x=0 to x=pi/3.

can someone please do the question T_T?

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

integrate (x^2-1)/(x^2+x-6)

awesome. thanks

i've done the question twice, and both times i got pi^2/4 - 2. But the answers says pi^2/4 + 2. I just wanted to double check here. :)

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