Calculus generally

Show without recourse to any calculating aid that 7^{1/2} + 7^{1/3} + 7^{1/4} < 7 and 4^{1/2} + 4^{1/3} + 4^{1/4} > 4 . Sketch the graph of f(x) = x^{1/2} + x^{1/3} + x^{1/4} -x

Third in our series of problems on population dynamics for advanced students.

First in our series of problems on population dynamics for advanced students.

Second in our series of problems on population dynamics for advanced students.

Fourth in our series of problems on population dynamics for advanced students.

Sixth in our series of problems on population dynamics for advanced students.

Can you sketch these difficult curves, which have uses in mathematical modelling?

Explore the properties of this different sort of differential equation.

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.