I am about to start university next week, where I will have a maths test just testing our mathematical ability. However, since I have been on a gap year, my maths skills have gone somewhat rusty, and this is me being polite to myself!
So, I was wandering if you guys could help me with a few maths problems? Please only feel free to answer which ever ones you can, and I am terribly sorry I am asking such a huge favour without contributing anything first. I have got the answers to the questions, but just don't know how to arrive to them!
1) Rearrange the following formula to give d in terms of D and f:
(2 / D - d) + (2 / D + d) = (1/f)
It does look simpler if you write it out!
The answer is d = (D^2 - 4Df)^(1/2)
2) Given that y = loge (Ae^(-Bx)), find x in terms of y, A and B.
The answer is 1/B(loge A - y)
3) Differentiate y = ln(3x^(2) +1) with respect to x.
The answer is 6x/(3x^(2) +1)
4) Differentiate y = (x^(2) + x)^(-2) with respect to x
The answer is -(4x+2)(x^(2)+x)^(-3)
5) By differentiating the relation x^2 + y^2 = e^k (where k is a constant) with respect to x, find dy/dx.
The answer is -x/y
I would really appreciate it you guys could help me out here, as I genuinely require some help.
Thank you everyone in advance