Looking at small values of functions. Motivating the existence of the Taylor expansion.

In this question we push the pH formula to its theoretical limits.

Investigate the mathematics behind blood buffers and derive the form of a titration curve.

How does the half-life of a drug affect the build up of medication in the body over time?

Is it true that a large integer m can be taken such that: 1 + 1/2 + 1/3 + ... +1/m > 100 ?

The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.

A weekly challenge concerning prime numbers.

What is the total area of the triangles remaining in the nth stage of constructing a Sierpinski Triangle? Work out the dimension of this fractal.

Which is the biggest and which the smallest of $2000^{2002}, 2001^{2001} \text{and } 2002^{2000}$?

Solve the equation sin z = 2 for complex z. You only need the formula you are given for sin z in terms of the exponential function, and to solve a quadratic equation and use the logarithmic function.

Compares the size of functions f(n) for large values of n.

Can you locate these values on this interactive logarithmic scale?