(See attached file for full problem description with symbols) --- Suppose is a matrix such that defines an element for . Show that . ---
(See attached file for full problem description with proper symbols) --- Let be the set of all sequences , such that exists. Let be the dual space of , and consist of all functions , , such that for every is finite. Let , and define such that . Show that is a one-to-one, onto bounded linear function ...continues
Cauchy-Riemann equations, vector gradients and contour lines
1. a) The Cauchy-Riemann equation is the name given to the following pair of equations, ∂u/∂x=∂v/∂y and ∂u/∂y= -∂v/∂x which connects the partial derivatives of two functions u(x, y) and v(x, y) i) if u(x, y) =e^x cosy and v(x, y) =e^x siny, how do I prove that these functions ...continues
1. From the function f (x)=IxI How would I go about finding its image set using interval notation? 2. Again using interval notation, how would I go about finding the image set of the graph g(x)= Ix+3I -2 ? And how then would I go on to solve the equation g(x)=1, and discover if it had any geometrical significance? 3. How ...continues
If I have the function f(x)=2e x+1 , how would I discover the domain and image set of function f? How would I go about finding the domain and image set of f -1? How would I go about solving the equation y= 2e x+1, to find x in terms of y?
Solution of the problem may require the use of L'Hospital's Rule (See attached file for full problem description)
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 ...continues
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 .
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.
