(6) If w = f(u, v), where u = x + y and v = x – y, show that = 2 ди

Q: If f(x,y,z)=xe^{4y}\sin(6z), then the gradient is

A:

Q: Find ôf af of and дх ду dz f(x, y, z) = 3×EYZ + 7yexz af -7 Əx af 7 ду af 3xe"y + 7yex %3D X ze

A:

Q: 2x :S dr f(x, y) dy. f (x, y) dy. •1-x² f (x, y) dy. -V1-r

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Q: Find fæ, fy, and fz. 4,5 f(x, y, 2) = 4z In (a*y° cos(5z))

A: We can answer all the three question as below.

Q: If f(x, y, z) = excosy + z, show that fxx + fyy + fzz = 0

A:

Q: B: Expressand as functions of u and v both by using the Chain Rule and by expressing z directly in…

A:

Q: Suppose z = f(x, y), where f is differentiable, a = g(t), and y = h(t). If g(3) · fy( – 2, – 6) = –…

A: Find dz/st when t=3

Q: 10. What is the work done moving a particle from x = 0 to x = 1 m if the force acting on it is F =…

A:

Q: 2. What is the relation between dV /dt and dr/dt if V = ()7r? %3D

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Q: xyz 3. If f(x, y,z)= In| +e 2 find f,, f, and f..

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Q: A function (f) is homogeneous of degree • if and only if : ôf + y = Af (x, y). Does the function…

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Q: Evaluate fSS 6e(²+y²+z²)/² dV over B where B= {(x, y, 2) : x² + y² + z² < 1}. Take T = 3.

A: Since we have    x2 + y2 + z2  expression in the integral and region B is the sphere of radius 1…

Q: Let F(z, v)-v +y+3z+1-0

A:

Q: 1 f(v) = , sec vtan v, F(0) = 4, 3 <V<-

A:

Q: Q2: Expand f(x,y) = [sin (x y³)]² about (5, 1).

A:

Q: Aşağıdaki alıştırmalarda, f., fy ve fiyi bulun. 23. f(x, y, z) = 1 + xy² – 2z2 25. f(x, y, z) = x -…

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Q: Determine (x, y) and 2(x, y), where f(x, y) = X sen(xy) %3D y

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Q: 2z Forz> 0, 순(/"m(P + 1) a) In (t³ + 1) dt For x > 0,

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Q: Find fz(x,y) and fy(x, y) given f(r, y) = csc yArcsin(r²).

A:

Q: 1 F (s) = s (s +1) %3D

A: Given: L-11ss+1

Q: Evaluate f, xyz dV, where Q = {(x, y, z): 0 < x < 2y, 0 <y< 1, 0 < z < x+y}.

A: According to question,Q = x,y,z : 0 &lt; x &lt; 2y, 0 &lt; y &lt; 1, 0 &lt; z  &lt; x+y

Q: 5. Given that f (x, y) = sin y, determine fy(x, y).

A:

Q: 2. Show that the function u = p(xy) + Vry ý(y/x) provides the equation n, = 0. dy? U -

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Q: Find f, and f,. f(x, y) = 13x In xy

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Q: Let x,(t)-v(t)+sin(r), x,-vt) then x,(t)= xN-cosit) Select ones True, False

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Q: Given : 6 (x, y, z) Compute the gradient = 3 6y³ z³ - 5 ex at PA (2,2,1-5) of G (x, y, z)

A: Given  G(x,y,z)=6y2z3-5e-x We have to find the gradient at the point PA(2,2,1.5)

Q: f(r, y, z) = byz In(4ry) %3D fz = fy = た=

A: Given:

Q: Find fr, fy and fz. f(x, y, z) = x – Vy² + z? |

A: Given f(x,y,z)=x-y2+z2. The objective is to find fx,fy and fz.

Q: Find fz and fy- f(z, 9) = [" 9eª dt f.(x, y) = f,(x, y) =

A:

Q: 7. f(x) = x² In x, f"'(x) 1 8. y = -, y" 1 .f"(q) 9. f(q) = 2g* 10. f(x) = /x, f"(x) 11. f(r) = /9 –…

A: The objective of the question is determine the derivative of the given function "y".

Q: Find fr and fy- f (x, y): 6e dt 4 fa(x, y) = fy(x, y) =

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Q: Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t). If g(4) = – 4, g'(4) = 9,…

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Q: (a) The function z depends on u and v so that z = (2u – 1)(1 –v)? , u = x + 2y and v = x – 2y az…

A:

Q: 3. If f(x, y,z)= In *yz +e tar's="), find f,,fy and f. . хуz

A: we have to find the partial derivative

Q: Let f(x, y, z)= = fz(x, y, z)= fy(x, y, z)= fz(x, y, z)= 2² - 2y² I y² + 4z² Then

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Q: Calculate fw(-1, 2, 0, –1) where f(x, y, z, w) = xy²z – xw² – e2a²-v²-²+2w²

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Q: Let f (x, y) = 2x³ + 4y³ + 19xy Find D = frx · fyy - fey at the point (2,2)

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Q: -2 X Given f(x,y,2) sin (z²y), show that fxyuy = fyxy %3D %3D

A: Given:- f(x, y, z) =e-2x sin(z2y)  To prove:- fxyy = fyxy

Q: Verify Young's Theorem S. f(x, y) = = e(2x+y) In(xy)

A:

Q: B. Use Green's theorem to evaluate f (x²y)dx + y²dy Where C is close path formed y = x and y = x³…

A: Above first question is solved. Solving more than one question is against the policy of bartleby.

Q: f (x, y, z) = x² + y² + z² and u = (1,0, 1) at P(1, 1, 1).

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Q: (ii)If y=(x+Jx* +1. prove that y'= Vx +1

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Q: Let f(r,y, z) = x² + 3x°y + z°, g(u, v) = (u² + v², uv, 3u – 2v). Find the derivative of f(g(u, v))…

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Q: Suppose f is differentiable at (3, 4), V f(3, 4) = (-V3, 1), /V3 and u = Compute D„f(3, 4). 2

A: ∇f3, 4=-3, 1, u=32, -12

Q: 2. Let f(x,y) 3x y. If C is the line segment from (1,1) to (2,3), evaluate r'dt.

A:

Q: Evaluate f(x, y, z) ds. Js f(x, y, z) = x2 + y2 + z2 S: x + y = 36, 0 SxS 6, OszS X %3D !3!

A: To evaluate:

Q: 9. If f(x,y) = -cos x+e*y, find Vf(x, y).

A: For the solution follow the next step.

Q: Consider the function: u = 2 ln /x² + y² Show that uzz + Uyy = 0. %3D

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.