2. Let A = {a, b, c}, B = {x, y, z},C = {r, s, t}. Let f : A → B and g : B → C be defined by:f = {(a, x), (b, z), (c, x)}, and g = {(x, t), (y,r), (z,r)}.Find(a) Composition functiongof : A→ C(b) Range of f, Range of g, Range of go f.

Answered: Image /qna-images/answer/be09531f-7d2b-4365-aef6-9b8305a32e6f.jpg

Answered: 2. Let A = {a, b, c}, B = {x, y, z}, C…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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5. Let f(x, y) = P(X =x,Y = y), X = 2,3,4, Y = 1,2,3,4, where P is given by the table below: X = 2 X = 3 X = 4 Y = 1 Y = 2 Y = 3 1/20 2/20 1/20 2/20 1/20 3/20 1/20 2/20 2/20 2/20 1/20 Y = 4 2/20 For problems (a) - (d) below write your work using the correct notation in terms of f (e.g. f(x, y), fy: f,(3), fyp fxp(4) ): (a) Verify that f is a joint probability mass function. (b) Find the marginal distribution for each random variable. Are both random variables independent? (c) Find the mean and variance of each marginal distribution. (d) Find the conditional probability function of Y given X =3. (e) Find E(Y|X = 3) and V(Y|X = 3). (f) Find P(X+Y =5), P(Y >1), and P(X +Y =5|Y > 1).
Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies. u(-9, 5) = -2 v(-9, 5) Vs(-9, 5) V(-9, 5) G,(-2, 3) : 3 Us(-9, 5) = 6 -4 = -1 = 4 G,(-2, 3) (s '6–)'n = -6 = -7 Find R,(-9, 5) and R,(-9, 5). R(-9, 5) R;(-9, 5) Need Heln? Read It
Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies. u(3,-2) = -6 us(3,-2) = 4 u(3,-2) = -7 Fu(-6, -4) = 0 v(3,-2) = -4 Vs(3,-2) = 9 v(3,-2) = 1 F(-6, -4) = 7 Find We(3,-2) and We(3,-2). Ws(3,-2) = W+(3,-2) =
1. Let f(x, y) =x+2y. Find f(0, 1), f (2, –1), f(a, a), and f(a + h, b) – f(a, b). 2. Let f(x, y) = xy². Find the respective values of f (0, 1), f(-1,2), f(104, 10-2), f (a, a), f(a+h, b), and f(a, b+ k) – f (a, b). %3D 3. Let f(x, y) = 3x² – 2xy+ y. Find f(1, 1), f(-2, 3), ƒ(1/x, 1/y), p = [f(x+h,y) – f(x, y)]/h, and q = [f(x, y + k) – f(x, y)]/k. %3D SECTION 11.2 / PARTIAL DERIVATIVES WITH TWO VARIABLES 411 4. Let f(x, y) = x² + 2xy + y². (a) Find f(-1,2), f(a, a), and f (a + h, b) – f(a, b). (b) Prove that f(2x, 2y) = 2f(x, y), and that f(tx, ty) = tf(x, y) for all t.
Let A=[t, t?,0] and B=[1, t2, 0] and C=[2,t3, 1] find (ABC)
Let the domain of x and y be all people. Let W(x): “x is a woman", M(y): "y is a man", and L(s.y): "y loves x". Then Vx3y, [(W(x) AM(y)) → L(x,y)] means Every woman is loved by all men. Every woman has a man that loves her. Every man has a woman that loves him. O Every man is loved by all women. O None of these
Find f, and , and evaluate each at the given point. fx, y, 2) - xy + 2xyz - 5yz, (-2, 1, 2) ,x, y. 2) - ,x, Y. 2) - 1,0x, v. z) - (-2, 1, 2) - ,(-2, 1, 2) - 1,(-2, 1, 2) -
Suppose that (S, 41) and (T , 42) are posets. Show that (S T , 4) is a poset where (s, t) 4 (u, v) ifand only if s 41 u and t 42 v. Show your work in details.
Find fy and f and evaluate each at the given point. Fx, y, 2) = x*y> + 2xyz - syz, (-2, 1, 2) (X, Y, 2) = f(x, y, z) - x, y, 2) - (-2, 1, 2) - -2, 1, 2) = 4-2, 1, 2) = %3D
Find f, and f, and evaluate each at the given point. f(x, y) = e*y?, (In 9, 2) f,(x, y) = 1,x, v) = f,(In 9, 2) = f,(In 9, 2) =

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2. Let A = {a, b, c}, B = {x, y, z}, C = {r, s,t}. Let f : A → B and g : B → C be defined by: f = {(a, x), (b, z), (c, x)}, and {(r, t), (y, r), (z, r)}. q = Find (a) Composition function go : A → C (b) Range of f, Range of g, Range of gof.