We need more information. Is there a limit or integral? The theorem states that the deivitive of an integral of a function is the function
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The purpose of calculus is to solve physics problems.
Calculus is interesting because it is incredible that human intelligence has discovered a way to solve a problem using a formula that can be repeated. Calculus is not necessarily about the numbers, but about the fact that we can apply rules and theories to numbers in a variety of situations.
Calculus Solved is software that is useful for learning calculus. It allows you to enter in problems and will walk you through how to solve each one. It also includes tests so you can track your progress.
Calculus was created to solve problems in physics that could not be solved given the mathematical methods available at the time. One of my teachers said that Newton invented Calculus to understand the laws governing planets' elliptical rotations around the sun.
A proof in calculus is when it will make a statement, such as: If y=cos3x, then y'''=18sin3x. Then it will tell you to do a proof. This means you have to solve the equation step by step, coming to the solution, which should be the same as in the statement. If you do come to the same answer as in the statement, then you just correctly did a calculus proof.