Calculus generally

Two circles of equal size intersect and the centre of each circle is on the circumference of the other. What is the area of the intersection? Now imagine that the diagram represents two spheres of equal volume with the centre of each sphere on the surface of the other. What is the volume of intersection?

Can you hit the target functions using a set of input functions and a little calculus and algebra?

Get started with calculus by exploring the connections between the sign of a curve and the sign of its gradient.

Consider these analogies for helping to understand key concepts in calculus.

Find the relationship between the locations of points of inflection, maxima and minima of functions.

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

Can you find the maximum value of the curve defined by this expression?

Can you find a quadratic equation which passes close to these points?

How would you sort out these integrals?