Category Archives: Applications

Calculus isn’t useless: When Velociraptors Attack

1. Some critics may sneer calculus is useless. Oh yeah? Well, we can solve this problem: Question: The velociraptor spots you away and attacks, accelerating at from a stand start, up to its top speed of . When it spots … Continue reading

Posted in Applications, Calculus, Differential, Integral, Optimization | 2 Comments

Area of a Surface of Revolution (Part 1)

1. Suppose we consider some function on the domain . For example: We revolve this about the axis by 360 degrees. So this looks like Question: what is the area occupied by this surface?

Posted in Applications, Calculus, Definite Integral, Integral | 2 Comments

Calculating Arc-Length of Curves

1. Recall we have some curve usually of the form . But sometimes we can write it as where both coordinates are a function of “time” . Convention: we will set . [Caveat: some exercises may have a different range … Continue reading

Posted in Applications, Calculus, Integral | 2 Comments