Prove that tan squared theta plus 1 equals sec squared theta. Use this identity to solve for tan theta if sec theta equals 5 over 3.
Define the union and intersection of two sets. If A is the set 1, 2, 3 and B is the set 2, 3, 4, find A union B and A intersection B.
A box contains 4 red, 3 blue, and 5 green balls. If two balls are drawn at random, what is the probability that both balls are green?
Define a differential equation and provide an example. Solve the differential equation dy over dx equal to 2x.
Define the area under a curve and explain how to calculate it using integration. Find the area enclosed between the curve y equals x squared and the x-axis from x equal to 0 to x equal to 3.
Explain the difference between indefinite and definite integrals. Evaluate the integral of x squared dx from 0 to 2.
Describe the process of finding the maximum or minimum of a function using derivatives. Find the maximum or minimum value of f of x equal to 3x squared minus 6x plus 7.