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...becomes a tangent to the graph of f at a point left parenthesis c comma f of c right parenthesis , where c lies somewhere between a and x . Clearly, the gradient of the original chord must be equal to the gradient of the tangent, so f of x minus f of a divided by x minus a equals f super prime of c full stop Multiplication by x minus a gives f of x equals f of a plus left...

...become turbulent and messy as a result of the vortices formed in the wake of the cylinder, but in the simulation the flow remains smooth. This difference is a consequence of assumptions made in the mathematical model describing the flow. Assumptions have been made to make the mathematics more manageable by neglecting the complexity that gives rise to the vortices....