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True or False? If true use short proof and if false use counter example d) The...
Please let me know whether true or false
If false, please give me the counter example!
(a) If a seriesE1an converges, then lim,n-0 an = 0. m=1 (b) If f O(g), then f(x) < g(x) for all sufficiently large . R is any one-to-one differentiable function, then f-1 is (c) If f: R differentiable on R (d) The sequence a1, a2, a3, -.. defined by max{ sin 1, sin 2,-.- , sin n} an converges (e) If a power series...
Question 8 (Chapters 1-8) [1 x 14 14 marks For the statements bellow, say if they are true or false. If true, give a short mathematical proof, if false, give a counterexample. (h) If f : Rn → R is convex and h : R → Rnxn s strictly convex and nondecreasing, then ho f is strictly convex (i) If f is strictly convex, then it is coercive. ) If f : Rn → R is such that the level...
Problem 1. Determine whether the following statements are True or False, and provide a short proof (or a counter-example) of your claim. (a) If A is an orthogonal matrix then A² is orthogonal. (b) If A2 is an orthogonal matrix then A is orthogonal.
Decide whether each statement is true or false and explain your reasoning. Give a counter-example for false statements. The matrices A and B are n x n. a. The equation Ax b must have at least one solution for all b e R". b. IfAx-0 has only the trivial solution, then A is row equivalent to the n x p, identity matrix. c. If A is invertible, then the columns of A-1 are linearly independent. d. If A is invertible,...
For intro to analysis. With short explanation please.
Thanks!
Mark the answers as "TRUE" or "FALSE" on the front sheet. 5. Let D C RP, and EC RP be open sets. Let F :D → E be a C1 function which is one-to-one and onto. Then the inverse function F-1: E + D is C1. 6. Let S C R4 be the solution set of the equation x2 + y2 = 22. Then S is a parameterized surface around the...
5. Determine whether the following statements are True or False. Justify your answer with a proof or a counterexample as appropriate. (a) The relation S on R given by xSy if and only if X – Y E R – N is an equivalence relation.
(10pts) 3. Use direct proof to show that if x and y are positive real numbers, then (x+y)" > " + y".
Problem E: For each of the following parts, state True or False. If true, give a short proof. If false, givera counterexample: (1). Using Kruskal's algorithm, edges are (always) inserted into the MST in the same order as using Prim's (2). If an edge e is part of a TSP tour found by the quick TSP method then it must also be part of the (3). If an edge e is part of a Shortest Path Tree rooted at A...
Math 32-_ Multivariable Calculus HW 3 (1) Consider the two straight lines L1 : (2-t, 3 + 2t,-t) and L2 : <t,-2 + t, 7-20 a) Verify that L1 and L2 intersect, and find their point of intersection. (b) Find the equation of the plane containing L1 and L2 (2) Consider the set of all points (a, y, z) satisfying the equation 2-y2+220. Find their intersection 0 and 2-0. Use that information to sketch a with the planes y =-3,-2,-1,0,...
1. (a) Which of the following is true and which is false? If you think a statement is true, provide a proof. Disprove those you think are false by giving a counterexample (i) A probability density function never exceeds 1 (ii) Suppose X and Y are two random variables defined on the same sample space, such that X > Y. This implies Var[X > Var Y] (ii) Let Z be a standard normal random variate N(0, 1). Then Z and...