4. Let f: X Y +R be any real valued function. Show that max min f(x,y)...
Find any global max or global min ) For the function f(x) = 2x3 - 6x2 +6 ;(-1<x<3)
3. Let the function f be a real valued bounded continuous function on R. Prove that there is a solution of the equation f(x) = x, xER. Now choose a number a with f(a) > a and define the sequence (an) recursively by defining al = a and a叶1 = f(an), where n E N. If f is strictly increasing on R, show that (an) converges to a solution of the equation (0.1). This method for approximating the solution is...
Convex Optimization Let f: R R be a differentiable function on R. Show that f is convex iff f' is nondecreasing (i.e. x y f'(x) <f'(y)).
true or false The real valued function f : (1,7) + R defined by f(x) = 2is uniformly contin- uous on (0,7). Let an = 1 -1/n for all n € N. Then for all e > 0) and any N E N we have that Jan - am) < e for all n, m > N. Let f :(a,b) → R be a differentiable function, if f'() = 0 for some point Xo € (a, b) then X, is...
Let f be a real-valued continuous function on R with f (-o0 0. Prove that if f(xo) > 0 for some zo R, then f has the maximum on R, that is, there exists an M R such that f(x) < f(xM) for al E R. Let f be a real-valued continuous function on R with f (-o0 0. Prove that if f(xo) > 0 for some zo R, then f has the maximum on R, that is, there exists...
Let g, h be two real-valued convex functions on R. Let m(x) = max{h(x), g(x)). Prove that m(x) is also convex 3.
Let n E Z20. Let a, b є R with a < b. Let y-f(x) be a continuous real- valued function on a, b]. Let Ln and R be the left and right Riemann sums for f over a, b) with n subintervals, respectively. Let Mn denote the Midpoint (Riemann) sum for fover la, b with n subintervals (a) Let P-o be a Riemann partition of a,b. Write down a formula for M. Make sure to clearly define any expressions...
f(x) Sa} 5. Show that if f is a convex function on R" then for any value a E R the set {<ER is convex, and so too is the set {x ER" f(x) <a}.
Can you help me with this question please? (5) (7.5 pts) Show that a complex-valued function f(r) is real-valued if and only if its Fourier coefficients An satisfy the conjugacy condition A-n-An. (5) (7.5 pts) Show that a complex-valued function f(r) is real-valued if and only if its Fourier coefficients An satisfy the conjugacy condition A-n-An.
1. Let B-(0, 1). Define x + y max(x, y) and x . y-min(x, y), and let the complement of x of be 1-x (ordinary subtraction). Show whether or not B forms a Boolean algebra under these operations. 2. Let S-(0,1 R, and T = { y : 2 < y < 12). Find a one to one correspondence (the actual function) between S and T showing they have the same cardinality. (hint: look at straight lines in the xy-plane)...