W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable. : 7, и( - 3, 2) — 6, o( — 3, 2) — 4, v.(- 3, 2) — 8, v:( — 3, 2) — — 9, 3, then find the following: If u( - 3, 2) — 5, и, ( — 3, 2) F(5, 4) 9, and F(5, 4) w.(3, 2) W3, 2) =

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Q: 13. If y (x, t) is a function of x and t, prove that i) L. =py (x, p) – y (x, 0) 2. ii) L =p°y (x,…

A: By Bartleby policy I have to solve first 3 subparts

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A: Given that,  fx,y,z=e2x+3y-4z+xyz And  x=3sinrty=2cosrtz=r2+t2 If F=fx,y,z, Where, x, y, z are…

Q: If f(x, y) = xsiny + e" , then V f(x, y) = (0, e'). Select one: True OFalse

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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A: Explanation of the answer is as follows

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A: Given :f(x,y,x)=3x-4y+6z

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A: See the attachment

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Q: If y = f(t, y(t)) = y(t) – t² + 1, then f'(t, y(t)) = (v- d -(v -t² + 1) = dt y- t? – 2t + 1 Select…

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Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies…

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Q: Which of the following is true if* f(x, y) = 2- 2xy + xy³ + 3y? frz (x, y) = 6x fyy (z, y) = 6+ 6xy…

A: Given that f(x,y)= x^3-2xy+xy^3+3y^2 then find the fxx, fyy, fxy.

Q: If r = g(t) , y = h(t) , z = f(x, y) , g(3) = 2 , g'(3) = 5 , h(3) = 7 dz 2. %3D , h'(3) = = 3, -4 ,…

A: Here , x=gt , y=ht , z=fx,yg3=2 , g'3=5 , h3=7 , h'3=-4 ,fx2,7=6 , fy=2,7=-8 and t=3

Q: Q3 Given that w = x + 2y + z²,x = = ,y = r2 + In s, z = 2r X%3D %3D aw aw and ar Find as

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Q: 4) Suppose that T : R³ → R² is defined by T((x, y, z)) = (1+2x – z , 3 – x + 6y) Is T linear?…

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Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.…

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Q: Given f(x, y, z) = V 4a? + 2y? + z², find fz(x, y, z) = fy(x, y, z) = f:(x, y, z) = |

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Q: Given f(2, y, z) =v V-I - 2y + z, find f.(z, y, z) = f(z, y, z) = f(1, y, z) =

A: We will use definition of differentiation. First we will handle derivative of the root of the…

Q: Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t). If g(5) = 8, g'(5) = 9, h(5)…

A: Given that z=fx,y, where f is differentiable. Here, x=gt and y=ht. Also, let, g5=8, g'5=9, h5=-7,…

Q: S F(2,v) For any function f(x, y) continuous on the ry-plane, f(r, y) dædy. O True False

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Q: 49. If f(u, v, w) is differentiable and u = x – y, v = y – z, and w = z – x, show that af af ду af…

A: Given f(u,v,w) is differentiable. By chain rule of differentiation , we have

Q: (a) Vx E R, 3y E Z such that y > x + 110. (b) Vx E Z, 3y E N such that y > x + 110. (c) 3x E Z such…

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Q: Given f(x, y, z) = V 42? + 6y² + 3z², find fz(x, y, z) = fy(z, y, z) = %D f:(x, y, z) =

A: we need to find out partial derivative of first order

Q: For x = 1, 2, 3 and y = 1, 2, let the joint pmf of X and Y be defined by fX,Y (x, y) = x + y/21…

A: Solution

Q: If L(x, y) is the local linear approximation of f(x, y)= x²+2y3+ 9:" at (2, 1) where g(2, 1) = 4,…

A: Given: f(x,y)=x2+2y3+g(x,y)x g(2,1)=4 gx(2,1)=4 gy(2,1)=6 At (2,1).…

Q: Given f(r, y, z) = – 5e 4ayz, find %3D fr(x, y, z) = f,(x, y, z) = f:(2, y, z) =

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Q: ( b) For n=1,2,K , show that (x² –1)y"*) +2(nx + p)y") +(n² –n)y"-1) =0 where %3D d" y p") = (Hint:…

A: * Given that y = x+1x-1pa dydx = px+1x-1p-1ddxx+1x-1    dydx = px+1x-1p-1x-11-x+1.1x-12   dydx =…

Q: Let z = 2³ + 3?, and let æ and y be functions of s and t with æ(0,0) = –1, y(0, 0) = 2, and ds dy =…

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Q: If F (x, y, z) = xyzî – e² cos xĵ + xy² z³k, what is V · (V×F) (1, 2, 3) 1 2

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Q: -E- x2 and S: R2 → R², 4. Let T : R² → R², x-y (a) Find (SoT)(u) where u := E R?. (b) Find a…

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Q: If z = f(r*y,2x) + g (E with f and g differentiable, then if u= r*y, w= 2r and t == Then: dz A) 2ry…

A: Given : z = fx2y, 2x + gxy with f and g differentiable. Also if u = x2y, w = 2x and t = xy.   To…

Q: Q3. If F = x'a, + y'a, + (z² – 1) a̟, find F· dS, where S is defined by r= 2, 0 < z < 2,0 < ¢ < 2r.

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Q: Suppose that z = f(x, y) is differentiable at the point (1024, 256) with f-(1024, 256) = 4 an dz…

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Q: -. Evaluate f. F dr where F(x,y, z) = e²i + xzj+ (x + y)k and C is given by r(t) = t²i + t°j- tk, 0…

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Q: e) Zs and zt, where z = xy – x²y, x = s + t, and y = s – t. [Ans:z, = 2s – 3s² – 2st + t²; z, = -s²…

A: We have to find derivative using chain rule. (e) zs and zt , where z=xy-x2y , x=s+t and y=s-t (f) zs…

Q: a the diagram, PU||QT, Ì = 42°, RQS = 82°, = v, UPT =r and QPT = x+40°. Prove that PT|QS. %3D P…

A: Given: PU||QT Concept: Pair of interior angles on the same side of the transversal are supplementary

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A: Given f(x,y,z) =xy+z , x=s2 , y=st and z=t2. We need to calculate -df/ds.

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Q: Given f(x, y, z) = V5x – 5y + 2z, find fa(x, y, z) =| %3D fy(x, y, z) = f-(x, y, z) =|

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Q: (a) z, and z4 where z = sin(2x) + y, x = s² – t², and y = s² + t² (b) z, and z4 where z = e*+y, x =…

A: We need to find the partial derivatives z.

Q: 2: find fr, fy, and fz. 9 f(x, y, z) = 1 + xy? - 222 5 f(x, y, z) = x - Vy² + z?

A: (a) Given f(x, y, z) = 1 + xy2 - 2z2 So fx = ddx(1 + xy2 - 2z2)    = ddx(1) + ddx(xy2) - ddx(2z2)…

Q: If f(x, y, z) = In(x° + yº + 2®) + v(x° + y8 + z®), then find f, fy and f; at (1,1, 1). %3D

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Q: . If z = f (x, y), where x = e" - e and y = e - e", show that TM UT az x: az az az dy ax UTM UTM UTM…

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Q: 4 - If w = x+ 2y + z? , x= , y =r2 + In(s) , and y = r2 + In(s) , and z = 2r aw find at the point…

A: Using chain rule the given question has been solved in step 2.

Q: Let f(x, y, z) = 3x?y+ yz3, where x = 3 – t2, y = 2t + t3, and z = V1+ 3t. Calculate when t = 1.

A: NOTE: Refresh your page if you can't see any equations. . here we have . the given function is…

Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.…

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Q: (b) Compute f er+uds, where c(t) = (t, 2t), t e [1, 2]. %3D

A: