f(x,y,z)=x+y+z and r(u,v)= (2u+ v, 3u - v, u+2v). What is the value of f(r(u,v)) r, xr, AA when u=2, v3, Au = 0.1 and Av 0.2 ?

Q: Compute div F, where F(x, y, z) = (x² + 3y, y? – 4z, sin r cos y – 22). A. (4 – sin r sin y, – cos r…

A: Given : F(x, y, z)=(x²  + 3y ,  y² -4z ,  sin(x )cos(y) - z2 )  Now we find div F = ?

Q: What is the directional derivative of f(x, y, z) = bx²y²z² + x² + y² + z² in the direction of v =…

A:

Q: Find fzyæ. f(r, y, 2) = a'y"2³ + xy® + y°z %3D f zyz

A: Given f(x,y,z)=x^4y^7z^5+xy^6+y^7z

Q: Vx? + yZ 49x2 49 [F,(x, y)]² + [f,(x, y)]² 1+ x² + y2 e have [f,(x, y)]² + [f,(x, y)]² = /

A: This is the question from vector calculus.

Q: What is the gradient of f(x, y, z) = x³₂² + y³z +125z - 1 at P(5,5,-1) ? 75i + 75k -75i - 75k 75i -…

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

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

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Q: Let F(x, y) =x2+xyz+z , find at the point (1,1,1)

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Q: Find the linear approximation to f(x, y, z) = at the point (–2, 3, 2) f(x, Y, z) ×

A:

Q: How is the linearization of f(x, y) centered at (a, b) defined?

A: To define linearization of a function f(x,y) at point (a,b).

Q: Find fzyz. f(r, y, z) = x*y³zª + xy" + y°z f zyz

A: Given-  fx,y,z=x4y3z4+xy7+y6z To Find- fzyx

Q: (a) f :Z → Z, where f(x) = x². g : Z → Z, where g(x) = |æ|². %3D (b) f :Z × Z → Z, where f(x, y) =…

A:

Q: Find fzya. f (r, y, 2) = x°y*z" 5.8 + xy* + y°z %3D f zyz

A: Given data÷

Q: Find fzyz. f (x, y, z) = x°y°z° + xy7 + y®z f zyz ||

A: Using derivative,

Q: Let f(x, y) = (- (3z + y))°. Then

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Q: Find the linear approximation to f(x, y, z) = at the point (2, –1, –2): f(r, y, z) z

A: A Givenfx,y,z=xyz at the point 2,-1,-2linear approximation at the point…

Q: Determine the local linear approx imation of flx,4,z) =(1+x) (l-y³) (l-2)²' at the point CT, 2,3)

A: The local linear approximation: Lx, y, z of the function f(x, y, z) at the point x0, y0, z0 is…

Q: Find Vf at the given point. f(x,y,z) = x² + y² - 4z²+zlnx, (1,1,3) Vf|(1,1,3) = i +(\)j + ()k…

A: Topic:- application of derivatives

Q: Find the linear approximation to f(x, y, z) = " at the point (2, -1,1): f(x, y, z) z

A: Given the function

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

A: Given:

Q: The gradient vector of the function f(x, y, z) = ln(yz) + x² is: Select one: ○ (2x,-1,-1/2) (2x₂ O…

A:

Q: The gradient of f(x, y) = xy at (x, y) = ( – 3, – 2) is %3D

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Q: The gradient of f(x, y) = xy at (x, y) = (2, 3) is

A:

Q: f(x, y, z) = e-3zyz 三 fy = 三 ニ f.

A:

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…

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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: The gradient of f(x, y) xy at (x, y) = (– 1, 1) is

A:

Q: Find the linear approximation to f (x, y, z) = 3, -3, – 1): at the point | F(x, y, z) ×

A:

Q: Find the linearization of f (x, y, z) = xy / z centered at (2, 1, 2). Use itto estimate f(2.05, 0.9,…

A: Our Aim is to find the linearization of f(x,y,z) =xyz centred at (2,1,2).and then using that value…

Q: Let f(z)=ex^2 = U(x,y)+iV(x,y) Verify Ux=Vy

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Q: Find the linearization of f(x,y) at the indicated point (X0,Yo): f(x,y) = In (x² + y); (1, 1) L(x,y)…

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Q: u:(x, t) = и (т, Urz(T, t) u,(0, t) = uz(1, t) = 0 u(x,0) = f(x)

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Q: ) Compute f-(, ") and fy(§, T) of f(r, y) = e9 cos(ry)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the linear approximation to f(x, y, z) = at the point (3, -2, -2): f(x, y, z) Z

A: To find the linear approximation of the below function at the point 3,−2,−2. fx,y,z=xyz

Q: (a) If F(v² – x²,v² – y², v² – z²) = 0 where v is a function of x, y,z show that 1 dv 1dv 1 dv 1 хдх…

A: Using chain rule.

Q: The gradient of f(x, y) = xy at (x, y) = (3, 1) is

A:

Q: Find the directional derivative of f (x, y, z) = xy²z³ at P(2,1,1) in the direction of Q(0,–3,5)

A: Solution: The objective is to find the directional derivative of the given function

Q: Find the directional derivative of f(x, y, z) = xy²z³ at P(4, 1, 1) in the direction of Q(0, –7, 9).…

A:

Q: f: (Z, +) → (Z, +) where f(x) = 2x. f: (R, +) → (R*, .) where f(x) = 2*

A: We will use definition of isomorphism

Q: tor. f(x,y)= In (8+3x²+3y²); P(3,-1); (3.2) d the gradient of f(x,y) = In (8+3x²+3y²). xx,y)=

A: Topic:- application of derivatives

Q: Find the linearization of f(x,y) at the indicated point (Xo.Yo). f(x,y) = In (x +y): (4, 5) L(x,y) =

A:

Q: The gradient of f(x, y) = xy at (x, y) = (3, 3) is

A: Given problem:- Find the gradient of f(x, y) =xy at (x, y) =(3, -3)

Q: z=f(x, y) = 2x +3 y at the point (2, 2, 20) (ii) Use a linear approximation to estima

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Q: 2xy F(x, Y) =Vx+ 2y (1, 1) f,(x, y) = 1,(1, 1) S(1, 1)

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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: Find the linearization of f(x,y) at the indicated point (X0:Yo). f(x,y) = In (x +y); (6, 1) L(x,y) =

A:

Q: Find the linearization of f(x,y) at the indicated point (X0.Yo)- f(x,y) = /x + 2y; (1,6) L(x,y) =

A: