how do we know calculus will provide the "answer" we seek? Is there any objective method to judge its accuracy? How do we know the solutions are correct and reliable? How do we know the professor is actually teaching us the correct methods for doing this stuff? Why isn't calculus taught as applied math instead of random problems? How does the student know if the grader is ignorant or if the his solution is wrong? How do we know that the person who wrote the book did so accurately according to Newton, and whether the "problem-creating algorithms" are reliable? How do we know the calculators that are programmed to "do calculus" can do it correctly? Are there different solutions to any given problem, or is there only one "right one"? How does the student or grader know that?