>>14338198The later chapters of Apostol's Calculus is great at this. In fact, he talks about this in the intro. Sample questions from the intro:
>With what speed should a rocket be fired upward so that it never returns to earth? What is the radius of the smallest circular disk that can cover every isosceles triangle of a given perimeter L? What volume of material is removed from a solid sphere of radius 2r if a hole of radius r is drilled through the center? If a strain of bacteria grows at a rate proportional to the amount present and if the population doubles in one hour, by how much will it increase at the end of two hours? If a ten-pound force stretches an elastic spring one inch, how much work is required to stretch the spring one foot?Just randomly choosing questions from the book:
>Given a sphere of radius R. Find the radius Y and altitude h of the right circular cylinder withlargest lateral surface area 2(pi)(r)h that can be inscribed in the sphere.
>Let (a1 , b1) and (a2 , b2) be two points in the plane such that a1 - a2 =/= n(pi), where n is an integer. Prove that there is exactly one solution of the differential equation y" + y = 0 whose graph passes through these two points.>A curve with Cartesian equation y = f(x) passes through the origin. Lines drawn parallelto the coordinate axes through an arbitrary point of the curve form a rectangle with two sides on the axes. The curve divides every such rectangle into two regions A and B, one of which has an area equal to n times the other. Find the function f.
You learn these types of complex/practical problems as you go, so you know how to break things into steps and solve.
