23. Let f(x, y) = xy² and let x(s, t) = t² ln(s) and y(s, t) = = s-t Compute of woivos Əs (s, t)=(2,1)

Q: If r'(t) = (1,21,3r*) and r(0) = (0,1,2) then r(t) equals %3D (a) (1,r°,r'). (b) (1,r",r')+ (0,1,2)…

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Q: Calculate r' (t) and T(t), where r(t) = (6 +5t,9 – 61, 2t). r' (t) = ( ). T(t) = ( ).

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Q: Find f'(2), where f(t) f'(2) = = u(t) · v(t), u(2) = (2, 1, −2), u'(2) = (7, 1, 8), and v(t) = (t,…

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Q: (x, y) = (b) 1 1 (d) 1/2 Does not exist. (x, y) = Ty³ x² + y6 = Find limf(x,y) along the path x =…

A: We will find the required.

Q: 1) Let f(z,y)- . Compute DS(z,y) where u- (4-9)

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Q: The equations xy² + 8xzcos(u) + ye" = 16 and xyz + xev – 9u?v² = 27 are solved for u and v as…

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Q: (B) If f(x,t) = fakt e-y²dy, then prove that kfx = ft.

A: (.)  Leibniz rule :  Given

Q: Let f (x, y) = zy(z²–y") (z²+y²) if (x, y) + (0,0) and f (0,0) = 0. af af (a) If (x, y) # (0, 0),…

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Q: Suppose f(x, y, z)=x+y+z, h(x,y) = (x + y, x³, y) and g(x) = (x,x²). Calculate d =z=of oho g(x). dx

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Q: If r(t) = , find r '(t), T(1), r ''(t), and r '(t) ✕ r ''(t).

A: Given  r(t) = <4t, 6t2, 2t3>

Q: 2. If F(x, y, z) = 2z3 – 3(x² + y²)z, then verify that Frx + Fyy + F2 = 0. %3D

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Q: Suppose f(x, y) = xy² + 4. Compute the following values: f(4,-5)= ƒ(−5, 4)= f(0,0)= ƒ(5,-5)= f(t,…

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Q: O Find Vf, where f(x, y, z) = = e¯(ax+by+cz) with a, b, c some constants.

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Q: Determine if f(x, y) is continuous at (0,0) where x²y² √x² + y² 0 f(x, y) =. if (x,y) = (0,0) if (x,…

A: To determine whether  is continuous at where

Q: If f(x,y,z) = e* and g(x,y,z) = y – z Then, V (fg) will be;

A: Given fx,y,z=ex, gx,y,z=y-z

Q: Compute (S ,g) where f(t)=1– 3r² , g(1)=t-ť'onV = C[0,1]. %3D

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Q: f(x, y) = ln(+1), g(x, y, z)= e²+y+²+z²+y³+2, h(w, x, y, z) = (4r+wy)²(z-7w). 14.67=(2,4), =…

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Q: Let f(x, y) = (x° + ay´, xʻy°, 2x+by), g(u,v,w) = (3u² + bv² + w°, uvw). Find the derivative of…

A: f(x,y)=(x3+ay2,x2y3,2x+by)g(u,v,w)=(3u2+bv2+w3,uvw)To Find: Derivative of f(g(u,v,w)) using the…

Q: If r(t) =  , find  r'(t), T(1), r''(t), and  r'(t) × r ''(t).

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Q: Let y: (0, 3] → R?, y(t) = (t,?V³) and I := ran y. Sketch T and compute L(T) :!!

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Q: Let h(æ, y) = f(x)g(y) + (9(y))² and suppose that f(1) = 5, f'(1) = 3, g(2) = 8, g'(2) = 10. Then…

A: Given function is - h(x,y) = f(x) g(y) + g(y)2             ............................(1)We have to…

Q: f(x, y, z) = z°y?lna fazyzz =? IIY -2z2 O A. 12y2z2 В. 2x2 -12yz O C. x2 y24 O D. x4

A: Partial derivatives

Q: Determine each of the following derivative values that involve functions that are defined in terms…

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Q: O Determine if f(x, y) is continuous at (0, 0) where x² y ² f(x, y)=√x² + y² 0 if (x, y) = (0,0) if…

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Q: Dete‎rmine if f (x, y) = ={(xsi‎n3y)/(x‎2+y6), (x, ‎y) ≠ (0, ‎0) ={1, (x, y) = (0, 0) is‎…

A: Solution: A graph for a function that's smooth without any holes, jumps, or asymptotes is called…

Q: dz (е) dz

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Q: Let F(x, y, z) = x³yz² – 6x?yz + 9xz – 5y°z. Find F %3D xyz Fxyz

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Q: Let g(x, y) = Vx²y². Find 1. g(1, 2) 2. g(4,1) 3. g(2, у) 4. g(x,2) 5. g(w, z – 1)

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Q: 9-10 Use the Midpoint Rule with n = 4 to approximate the integral. tare ople setugmos B 8 • f₁x² dx…

A: Use the Midpoint Rule approximation formula.…

Q: The equations xy2 + 6xzcos(u) + ye" = 12 and x³yz + xe" - 8u²v² = 24 are solved for u and v as…

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Q: 4 Find f. (x, y) and f,(x, y) for f(x, y) = (5a³ – 4y²)*. f.(x, y) = Preview f,(x, y) = Preview

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