Q3. Q6. Using the definition of Ye,me(0,0) = (-1)me, (24+1)(-me)! 4TT (+me)! Ol,me (Oºm,(Ø), show that...
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b) i. Using e-8 definition show that f is continuous at (0,0), where f(x,y) = {aš sin () + yś sin () if xy + 0 242ADES if xy = 0 ii. Prove that every linear transformation T:R" - R" is continuous on R". iii. Let f:R" → R and a ER" Define Dis (a), the i-th partial derivative of f at a, 1 sisn. Determine whether the partial derivatives of f exist at (0,0) for the following function. In...
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zain Jo. Ø 73 3:45 • nering Q1: a function with the name "Area Circumference to calculate the area and circumference tput) of a rectangle. Define the inputs of this function as required. (6marks) Write a manuscript to solve the following system of equations based on (A]x] =[b]. Find x1, x2 4. (5 Marks) 2x1 + x2-03 + 2x4 = 5 4x1 +5x2-3x3 + 6x4 = 9 -2x1 +5x2 - 2.03 + 6x4 = 4 4x1...
3.2) (0,0) (24) 6,4) (0,) In the extensive form representation of the game between Player 1 and Flayer 2 Player 1 moves first and chooses L or R. If Player 1 chooses R the game ends, if Player 1 chooses L then Player 1 and 2 play a simultaneous move game. The game has pure strategy Nash equibra and pure strategy Subgame Pertect Nash Equnbia (SPNE). The maximum payott Flayer 2 gete in a SHNE IS Please, enter oniy numencal...
Question 1 10 points Using the definition of the transform, determine the transforms for each of the following signals. Sketch the pole-zero plot and indicate the region of convergence. (a) (5 points) (-3)"[n-2 () (5 points) "0(9) 15 points transforms for each of Question 2... Using 3-transform pairs and properties tables, determine the the following signals. (a) (5 points) un-un-2 (b) (5 points) -- [n - 2 (e) (5 points) nyin-1 ... 10 points Question 3 Find the inverse (a)...
Question 3 Consider the triangle constructed from the points () = (0,0), Q = (2,0) and P = (L cos 0, L sin (). (a) Write a function for the area of the triangle in terms of 0 and L, namely A(0, L). 3 (b) Show that if the triangle has a perimeter of 6 then L = 2 - cose (c) Sketch the domain of A on a OL-axes to ensure that the following conditions hold • L represent...
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EXERCISES FOR SECTION 2.5 1. For each of the following statements, determine whether it is true or false and justify your answer. a. Every bounded set is closed. b. Every closed set is bounded. c. Every closed set is compact. d. Every bounded set is compact. e. A subset of a compact set is also compact. 2. For each of the following statements, determine whether it is true or false...
$24 $6 Show that AR = P by definition. 2. 3. The firm faces a fixed cost of $2 per week, and the following variable costs. Complete the table below. Profit MR. Quantity of output (Q) TR ($) MC (S) TC (S) vC (S) FC ($) ($) ($) 0 2 2 0 6 10 8 2 1 12 2 12 10 2 2 18 15 13 3 24 19 17 30 5 24 22 36 6 30 28 2 6...
2. (10 points) Given the following functions: f()= r* - 50x3 +1, g(x) = 24 Show that f(x) = N(g(2) using the definition of 10. Do not forget to provide the witnesses.
1. [5 marks Show the following hold using the definition of Big Oh: a) 2 mark 1729 is O(1) b) 3 marks 2n2-4n -3 is O(n2) 2. [3 marks] Using the definition of Big-Oh, prove that 2n2(n 1) is not O(n2) 3. 6 marks Let f(n),g(n), h(n) be complexity functions. Using the definition of Big-Oh, prove the following two claims a) 3 marks Let k be a positive real constant and f(n) is O(g(n)), then k f(n) is O(g(n)) b)...