Search over 10,000 free study notes

8 traditionally has 1 cube root. 2. This is only the real root. It has 2 more complex roots!How can we see this?Consider a vector on the argand diagram. If we square it. What happens to it's magnitude and...

First take log’s each side as it would turn our complicated function into something differentiable by chain rule.
ln y = x*ln x
Then differentiate y with respect to x:
d(ln y)/dx = ln x + 1...

Prove the basis to be true. Let n=1 and this gives f(1)=16+375=391 which is divisible by 17. Now assume that if we let n=k f(k) is divisible by 17. If we now let n=k+1 and prove f(k+1) is divisible by 17 ...

Solving the ansatz equation x^2 - 4x + 3 = gives 2 equal roots where x = 3 and x = 1The general solution therefore is y = Ae^3x + Be^x where A and B are arbitrary constants

If you have studied Physics, you may be familiar with the small angle approximation cos θ ≈ 1 - θ²  / 2. This is a surprisingly accurate approximation for small values of theta (try it!), but w...