Search over 10,000 free study notes

Product rule: first order derivative = 8xlnx+4x Second order derivative = 8lnx+12 Sub in e^2 , 16lne + 12 = 24

First off, we better convert the 30mm into m. Now, we know that in 1cm there are 10mm. So in 2cm, there are going to 20mm and in 3cm there are going to be 30mm. So each textbook is really 3cm thick. Now, ...

We need calculus to find out the properties complex curves that we cannot find with simple arithmetic as we would with linear graphs. Differentiation allows us to calculate the gradient of a curve at a sp...

This is a quadratic equation of the form ax^2 + bx +c, where (t-1)=a 4=b . (t-5)=0 Therefore if there are no real roots, you get that b^2-4ac<0. (using the quadratic formula)

First plug in valu...

This is a good candidate for integration by parts because it is a product of two functions – ln(x) and x^3, and x^3 is easy to integrate. The definition for integration by parts is: integral(u dv/dx) d...