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Questions 1 and 2 1. Find the gradient of f(I, y) = sin(Zy+5). 2. Let f(x,...
Questions 1 and 2
1. Find the gradient of f(I, y) = sin(Zy+5). 2. Let f(x, y, z) - ryz + x) (a) Find the gradient of f. (b) Find an equation of the tangent plane to the level surface ryz + 2 = 5 at the point (2,1,1).
QUESTION 12 Let the random variable X and Y have the joint p.d.f. f(x,y) =(zy for...
QUESTION 12 Let the random variable X and Y have the joint p.d.f. f(x,y) =(zy for 0< <2, 0 < y <2, and z<y otherwise Find P(0KY <1) 16 QUESTION 13 R eter to question 12. Find P(o < x <3I Y-1).
in 3rd question it ask "z=z(x,y), if Z=x*f(y/x) proof x*Zx+y*Zy=z equation " and in 4th question...
in 3rd question it ask "z=z(x,y), if Z=x*f(y/x) proof
x*Zx+y*Zy=z equation "
and in 4th question it ask draw integration area, calculate the
integration and change integration line.
(x,y)–(0,0) x2 + y 3) = = z (x,y) olmak üzere z = xf (9) ise 2 tyzy = oldi 4 2 Dj sin (2²) dady 0 y/2
Q5. Suppose the joint pdf of X, Y is given by f(x, y) zy/3 if 0...
Q5. Suppose the joint pdf of X, Y is given by f(x, y) zy/3 if 0 s S1 and 0 sy< 2 and f(x,y) elsewhere. a. Compute P(X+Y2 1). b. What is the probability that (X, Y) E A where A is the region bounded above by the parabola y 2 c. What is the probability that both X, Y exceeding 0.5? d. What is the probability X will take on values that are at least 0.2 units less than...
(1 point) If f(x, y) = x*ey, compute the partial derivatives: fær(1, 3) = fyy(1, 3)...
(1 point) If f(x, y) = x*ey, compute the partial derivatives: fær(1, 3) = fyy(1, 3) = fry(1,3) = fyz (1, 3) =
QUESTION 23 If f(x, y) = x sin(xy?), compute fу (п. 1). ОА. - ОВ. -8...
QUESTION 23 If f(x, y) = x sin(xy?), compute fу (п. 1). ОА. - ОВ. -8 ос. -2 OD" - ОЕ. — бл
Find the volume of the solid bounded above by the graph of f(x, y) zy sin(z’y)...
Find the volume of the solid bounded above by the graph of f(x, y) zy sin(z’y) and below by the xy-plane on the rectangular region R = {(2, y) 0<x< 1.1547, 0 <y< 0.757}. Double Integral Plot of integrand and Region R 37 2 N 11 -0.20 0.2 0.4 0.6 0.8 1.0 1.2 Х This plot is an example of the function over region R. The region and function identified in your problem will be slightly different. Answer (to 4...
Find all the first and second order. partial derivatives of f(x, y) = 8 sin(2x +...
Find all the first and second order. partial derivatives of f(x, y) = 8 sin(2x + y) - 2 cos(x - y). A. SI = fr = B. = fy = c. = f-z = D. = fyy = E. By = fyz = F. = Sxy=
Question 2 (20 points): Consider the functions f(x, y)-xe y sin y and g(x, y)-ys 1. Show f is differentiable in its domain 2. Compute the partial derivatives of g at (0,0) 3. Show that g is not d...
Question 2 (20 points): Consider the functions f(x, y)-xe y sin y and g(x, y)-ys 1. Show f is differentiable in its domain 2. Compute the partial derivatives of g at (0,0) 3. Show that g is not differentiable at (0,0) 4. You are told that there is a function F : R2 → R with partial derivatives F(x,y) = x2 +4y and Fy(x, y 3x - y. Should you believe it? Explain why. (Hint: use Clairaut's theorem)
Question 2...
F(x, y) = (3x2 + sin y)i + (x cos y + 2 sin y)j. Question...
F(x, y) = (3x2 + sin y)i + (x cos y + 2 sin y)j. Question 1 (8 points) Find a potential function for the vector field F. Enter this function in the answer box. - Format B I U , . A X Question 2 (6 points) Use the potential function you found in problem 1 to evaluate F. dr, where Cis given by r(t) = (2-t)i + (ret/2), 0 st < 1.
Questions 1 and 2
1. Find the gradient of f(I, y) = sin(Zy+5). 2. Let f(x, y, z) - ryz + x) (a) Find the gradient of f. (b) Find an equation of the tangent plane to the level surface ryz + 2 = 5 at the point (2,1,1).
QUESTION 12 Let the random variable X and Y have the joint p.d.f. f(x,y) =(zy for 0< <2, 0 < y <2, and z<y otherwise Find P(0KY <1) 16 QUESTION 13 R eter to question 12. Find P(o < x <3I Y-1).
in 3rd question it ask "z=z(x,y), if Z=x*f(y/x) proof
x*Zx+y*Zy=z equation "
and in 4th question it ask draw integration area, calculate the
integration and change integration line.
(x,y)–(0,0) x2 + y 3) = = z (x,y) olmak üzere z = xf (9) ise 2 tyzy = oldi 4 2 Dj sin (2²) dady 0 y/2
Q5. Suppose the joint pdf of X, Y is given by f(x, y) zy/3 if 0 s S1 and 0 sy< 2 and f(x,y) elsewhere. a. Compute P(X+Y2 1). b. What is the probability that (X, Y) E A where A is the region bounded above by the parabola y 2 c. What is the probability that both X, Y exceeding 0.5? d. What is the probability X will take on values that are at least 0.2 units less than...
(1 point) If f(x, y) = x*ey, compute the partial derivatives: fær(1, 3) = fyy(1, 3) = fry(1,3) = fyz (1, 3) =
QUESTION 23 If f(x, y) = x sin(xy?), compute fу (п. 1). ОА. - ОВ. -8 ос. -2 OD" - ОЕ. — бл
Find the volume of the solid bounded above by the graph of f(x, y) zy sin(z’y) and below by the xy-plane on the rectangular region R = {(2, y) 0<x< 1.1547, 0 <y< 0.757}. Double Integral Plot of integrand and Region R 37 2 N 11 -0.20 0.2 0.4 0.6 0.8 1.0 1.2 Х This plot is an example of the function over region R. The region and function identified in your problem will be slightly different. Answer (to 4...
Find all the first and second order. partial derivatives of f(x, y) = 8 sin(2x + y) - 2 cos(x - y). A. SI = fr = B. = fy = c. = f-z = D. = fyy = E. By = fyz = F. = Sxy=
Question 2 (20 points): Consider the functions f(x, y)-xe y sin y and g(x, y)-ys 1. Show f is differentiable in its domain 2. Compute the partial derivatives of g at (0,0) 3. Show that g is not differentiable at (0,0) 4. You are told that there is a function F : R2 → R with partial derivatives F(x,y) = x2 +4y and Fy(x, y 3x - y. Should you believe it? Explain why. (Hint: use Clairaut's theorem)
Question 2...
F(x, y) = (3x2 + sin y)i + (x cos y + 2 sin y)j. Question 1 (8 points) Find a potential function for the vector field F. Enter this function in the answer box. - Format B I U , . A X Question 2 (6 points) Use the potential function you found in problem 1 to evaluate F. dr, where Cis given by r(t) = (2-t)i + (ret/2), 0 st < 1.
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