2 r(x) = | etat 4. (5 points each) Discuss the differentablity at x-0 for each...
JU 2. [5 points) If w = 63+4(.22 + 3j2) and x = (r – s) and y = (r +s)?, then the value of when r=1 and s=0 is (A) 244 (B) 1864 (C) 24e (D) 284 (E) 2224 (F) none of (A) - (E)
Problem 4 (4 points each). Let S = R {0}. (a) Let f: S R be f(x) = cos(1/x). Show that lim-0 f(x) does not exist. (b) For any fixed a > 0, let f: S+R be f(x) = rºcos(1/x). Show that lim -- f(x) = 0. (c) Find a value be R for which the function f: R+R given by f(x) = { 2" cos(1/x) if r +0, if x = 0, is continuous at 0. Is this b...
The monotonicity property of the integral implies that if the functions g,h : 0,00) → R are continuous and g(x) S h(x) for all x 2 0, then ghfor all r 2 0. 0 0 Use FTC1 to show that each one of the following inequalities implies its successonr: cosx <1 if r 0 1 - cosr if x 0 2 3 > if r 20 Hence The monotonicity property of the integral implies that if the functions g,h :...
3. (5 points for each Em and IN, 4 points for each Rm and Rn.) R R₂ um E o {R & R4 M Rs Ro In the circuit on this page, E: =168 V, R1 = 60, R2 = 27 0, R3 = 35 A, R4 = 34. , Rs = 3 0, R6 = 230 3a. Assume that R4 is the load. Fill in the table with the proper values as seen by Rs. ETH IN Rn RN...
2. Prove the following useful properties of Dirac δ-functions (a) δ(ax) = (z) (b) zfic) =0 (c) f(x)5(-a) f(a)5(r d) δ(z-a (aメ0) a) ( dz9(x-a) ) where θ(x) is the step function defined as 1 if r 0 0 if r <0 θ(z) = 2. Prove the following useful properties of Dirac δ-functions (a) δ(ax) = (z) (b) zfic) =0 (c) f(x)5(-a) f(a)5(r d) δ(z-a (aメ0) a) ( dz9(x-a) ) where θ(x) is the step function defined as 1 if...
3. (a) (5 points) On the set A= R\{0}, let x ~ y if and only if x · y > 0. Is this relation an equivalence relation? Prove your answer. (b) (5 points) Let B = {1, 2, 3, 4, 5} and C = {1,3}. On the set of subsets of B, let D ~ E if and only if DAC = EnC. Is this relation an equivalence relation? Prove your answer.
002 10.0 points Find the Jacobian of the transformation T: (r, 0) + (x, y) when x = e" cose, y = 2e-" sin . 1. O(x, y) = 2 cos 20 a(r, 0) 2. 8(x, y) a(r, 0j = -3e2r 2(x, y) a(r, 0) = -2 cos 20 4. (x, y) = 2 4. Əlr, o) 5. 0(x, y) = 3er cos 20 5. Ə(r, ) 2(x, y) - 2.21 DA a(r, 0) = -3e4
Computer architecture Having the next Boolean functions: F1(x,y,z)-П (1, 3, 5) . F2(x,y,z)-Σ (0, 2, 4, 5) . 1. Make one logic gate design circuit, using AND, OR and NOT logic gates (20 points). 2. Design two 4-to-1 selectors, one for each Boolean function (20 points) 3. Design one 3-to-8 decoder to solve both Boolean functions (20 points) 4. Design a 8x2 ROM to solve both Boolean functions (20 points) 5. Design a 3x5x2 PLA to solve both Boolean functions...
3. (8 points, 4 points each) f(x)-2x - 1 and g(x)-3x + 4, are functions from R to R. Find a. fog b. gof