Homework Answers
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17. For f(x, y)=e***+y)? of Ox? XZ of 18. For f(x, y, z)= =? y +...
17. For f(x, y)=e***+y)? of Ox? XZ of 18. For f(x, y, z)= =? y + z oz 19. For f(x, y, z) = cos’ (3x – y’) – x’ tanz, ar ax of = ? 20. For S(x, y) = x cos y + ye", дхду
8Two vector fields are given: F(x,y,z) - (esin(yz), ze* cos(yz), ye* cos(yz)) and F(x,y,z) = (z...
8Two vector fields are given: F(x,y,z) - (esin(yz), ze* cos(yz), ye* cos(yz)) and F(x,y,z) = (z cos y, xz sin y, x cos y). a) Determine which vector field above is conservative. Justify. Foly = fjol so, <ea sin(J2), 20% cos(82), y acos (92)) Conservative. b) For the vector field that is conservative, find a function f such that F - Vf. Lxelsing2, zetos yea, yet cosy 2 c) Use the Fundamental Theorem of Line Integrals to find the work...
please answer both parts - (a) (10 points) Find the maximum value of f(x, y, z)...
please answer both parts
- (a) (10 points) Find the maximum value of f(x, y, z) = xy + yz+xz on the plane x+y+z= 6 using Lagrange multipliers. No credit given for any other method. (10 points) Explain why the extremum found in part (a) is a maximum. Hint: turn the problem in part (a) into one involving 2 variables.
If z = f(x, y) is implicitly defined by the equation xyz + x-ye? – 3y...
If z = f(x, y) is implicitly defined by the equation xyz + x-ye? – 3y = 1, find the maximum rate of change of f(x, y) at the point (2,1). Please select file(s) Select file(s)
(1 point) х Suppose w 9 y + where у 2 + sin(2t), and z =...
(1 point) х Suppose w 9 y + where у 2 + sin(2t), and z = z X = e e5t, y 2 + cos(7t). as X. dw A) Use the chain rule to find as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite e e5t d dw 5/y(e^5t)+-x/y^2+1/z(2cos(2t))+(-y/3^2)*(-7sin(7t)) dt Note: You may want to use exp() for the exponential function. Your answer should be...
Question4 please (1). Let f: Z → Z be given by f(x) = x2. Find F-1(D)...
Question4 please
(1). Let f: Z → Z be given by f(x) = x2. Find F-1(D) where (a) D = {2,4,6,8, 10, 12, 14, 16}. (b) D={-9, -4,0, 16, 25}. (c) D is the set of prime numbers. (d) D = {2k|k Ew} (So D is the set of non-negative integer powers of 2). (2). Suppose that A and B are sets, C is a proper subset of A and F: A + B is a 1-1 function. Show that...
4. (5 points) (a): Find all second partial derivatives of f(x, y) = re-2ry, (b): Find...
4. (5 points) (a): Find all second partial derivatives of f(x, y) = re-2ry, (b): Find dw/dt at t = 1 if w = re + y sin z - cosz, r= 2/t, y=t-1+ lnt, and 2 = t.
Letf(r, y. z).(2xve, + yen.x,z, + xe".3x, yt, +cos:). a. Please find (2y+ye 5. С:/(r)-(cost.sin 1,1). Osis". dy b. Please to prove that F is a conservative vector field: ye". c....
Letf(r, y. z).(2xve, + yen.x,z, + xe".3x, yt, +cos:). a. Please find (2y+ye 5. С:/(r)-(cost.sin 1,1). Osis". dy b. Please to prove that F is a conservative vector field: ye". c. Please find J2xye d. Please find the potential function fx, y, z) such that F Vf e. Use the part (d) to evaluate F dr along the given curve C. f. Please find curlF g. Please find curlF
Letf(r, y. z).(2xve, + yen.x,z, + xe".3x, yt, +cos:). a. Please...
Given the function f(x, y, z) = xy +xz write f (x, y, z) as a...
Given the function f(x, y, z) = xy +xz write f (x, y, z) as a sum of min terms and a product of max terms.
(4) Let X,YX,Y be iid Uniform(−1,1) random variables. Find the density of Z=X+Y, and find the...
(4) Let X,YX,Y be iid Uniform(−1,1) random variables. Find the density of Z=X+Y, and find the characteristic function of Z. By using the inversion formula deduce that .∫0∞(sintt)2dt=π2. The following ``answers'' have been proposed. Please read carefully and choose the most complete and accurate option. (a) The characteristic function of X is sint/t. The characteristic function of Z is (sint/t)^2, which is integrable. If fZ(x) is the density of Z then fZ(x)=12π∫−∞∞(sint/t)^2 e^−itx dt. On the other hand, Z has...
17. For f(x, y)=e***+y)? of Ox? XZ of 18. For f(x, y, z)= =? y + z oz 19. For f(x, y, z) = cos’ (3x – y’) – x’ tanz, ar ax of = ? 20. For S(x, y) = x cos y + ye", дхду
8Two vector fields are given: F(x,y,z) - (esin(yz), ze* cos(yz), ye* cos(yz)) and F(x,y,z) = (z cos y, xz sin y, x cos y). a) Determine which vector field above is conservative. Justify. Foly = fjol so, <ea sin(J2), 20% cos(82), y acos (92)) Conservative. b) For the vector field that is conservative, find a function f such that F - Vf. Lxelsing2, zetos yea, yet cosy 2 c) Use the Fundamental Theorem of Line Integrals to find the work...
please answer both parts
- (a) (10 points) Find the maximum value of f(x, y, z) = xy + yz+xz on the plane x+y+z= 6 using Lagrange multipliers. No credit given for any other method. (10 points) Explain why the extremum found in part (a) is a maximum. Hint: turn the problem in part (a) into one involving 2 variables.
If z = f(x, y) is implicitly defined by the equation xyz + x-ye? – 3y = 1, find the maximum rate of change of f(x, y) at the point (2,1). Please select file(s) Select file(s)
(1 point) х Suppose w 9 y + where у 2 + sin(2t), and z = z X = e e5t, y 2 + cos(7t). as X. dw A) Use the chain rule to find as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite e e5t d dw 5/y(e^5t)+-x/y^2+1/z(2cos(2t))+(-y/3^2)*(-7sin(7t)) dt Note: You may want to use exp() for the exponential function. Your answer should be...
Question4 please
(1). Let f: Z → Z be given by f(x) = x2. Find F-1(D) where (a) D = {2,4,6,8, 10, 12, 14, 16}. (b) D={-9, -4,0, 16, 25}. (c) D is the set of prime numbers. (d) D = {2k|k Ew} (So D is the set of non-negative integer powers of 2). (2). Suppose that A and B are sets, C is a proper subset of A and F: A + B is a 1-1 function. Show that...
4. (5 points) (a): Find all second partial derivatives of f(x, y) = re-2ry, (b): Find dw/dt at t = 1 if w = re + y sin z - cosz, r= 2/t, y=t-1+ lnt, and 2 = t.
Letf(r, y. z).(2xve, + yen.x,z, + xe".3x, yt, +cos:). a. Please find (2y+ye 5. С:/(r)-(cost.sin 1,1). Osis". dy b. Please to prove that F is a conservative vector field: ye". c. Please find J2xye d. Please find the potential function fx, y, z) such that F Vf e. Use the part (d) to evaluate F dr along the given curve C. f. Please find curlF g. Please find curlF
Letf(r, y. z).(2xve, + yen.x,z, + xe".3x, yt, +cos:). a. Please...
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