L'Hospital's Rule

Solution of the problem may require the use of L'Hospital's Rule (See attached file for full problem description)

Prove

1- prove or disprove by giving a counterexample: "If 2 medians of a triangle are of the same lenght, then the triangle is isosceles"

One of the archeologists you interviewed for your article..

One of the archeologists you interviewed for your article is graphing asymptotes to illustrate the data generated through carbon dating the half-life of fossil specimens.Help him with his work by solving these problems: 1. Explain and contrast the types of asymptotes considered for rational functions. 2. Browse through some newspapers or magazines and find a situation that fits an exponential function . Explain why that data or situation fits an exponential function.

Compactness with two equivalent norms

(See attached file for full problem description and symbols) --- Assume that and are two equivalent norms on X, and that . Prove that M is compact in if and only if M is compact in .

Maximum and Minimum theorem

Prove: A continuous mapping T of a compact subset M of a metric space X into assumes a maximum and a minimum at some points of M.