Search over 10,000 free study notes

Take the integral as 1 x ln(x) instead of just ln(x). Use integration by parts giving two terms, the first is now just xln(x) and the second is the integral of 1 dx. This is easy to integrate giving the f...

So, basically |z| = 1 is equal to the set containing all complex numbers where their magnitude is equal to one. Also, by unraveling the definition of |z| we get that (x²+y²)^1/2<...

The answer to this question is in two parts. We firstly must find the derivative of the function y=f(x) with respect to x, and then substitute the value of x given in the question to find the gradient at ...

We differentiate y with respect to x:Firstly, we apply the Chain rule in the fist part of the RHS. Remembering the chain rule is uv -> u'v+uv', so d(3xe^{3x^2})/dx=3e^{3x^2}+18x^{2}e^{3x^2}now, we sim...

Resolving perpendicular to the plane: R - mg cos30 = 0. Therefore, R = m g cos30, where R is the reaction force perpendicular to the plane. Res...