2. Let f(r,y) = n: Find the maximum rate of change of f(r, y) at the point (4, 1) and the direction in whìch ít occurs.

Q: 3) Find the maximum rate of change of f at the given point P and the direction in which it occurs.…

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Q: The value of local acceleration in the x direction for flOW with all wrong u = 2(1 + t) is given by…

A: Given that  u=2(1+t)  To find the local acceleration in the x direction of flow

Q: Allow f(x, y) = xe^(xy), now find the maximum rate of change of f at the point (3, -1).

A:

Q: If f(x, y, z) = x² +y² – 4.xz, find the rate of change of f at P(3, 1, –2) in the direction from P…

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Q: Find the direction at which the function f(x, y, 2) = a In(e-az) increases fastest at (-3,0, 0) O…

A:

Q: Suppose that the temperature in a given region is given by T(x,y)=200xy(1-x2-2y2). Suppose that you…

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Q: Let f(z, y) = re". What is the maximum rate of change of f at the point (2,0)? O a. V5 O b. 2 O c. 1…

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Q: Please find the gradient of f(x, y) = ln(x² + xy²) at (2, 1)

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Q: consider the function f(x, y) = esin(x), Find the maximum rate of change of f at the point (, 1).

A: The direction of maximum increase of f is given by ∇fx,y.Maximum value of Du→fx,y or rate of…

Q: (a) Find the derivative of f(x, y, z) =x²- xy²- z at Po(5, 1, 0) in the direction of v=2i-3j+ 24k.…

A: Given: f(x, y, z) = x2 - xy2 - z, P0(5, 1, 0) and v=2i - 3j + 24k.

Q: integrate ​f(x,y)=x2−y over the curve​ C: x2+y2=4 in the first quadrant from (0,2) to 2,2.

A: The solution are next step

Q: Find the maximum rate of change of the function f(x, y, z) = xy + yz - xz at the point P,(1, -3, 4).

A: As per our guidelines we are supposed to answer only one question.

Q: e) The maximum rate of change of f(x, y) at the point (x, y) = (1, 0) is

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Q: Find the direction in which f (x, y, z) = z exy increases most rapidly at the point (0, 1, 2). What…

A: We have given f(x, y, z) = zexy and the point (0, 1, 2).

Q: F(X, y,z) = 2x -y? +z?

A: F(x,y,z)= 2x-y^2-z^2 at point (4,-4,2) df/dx= 2 df/dy=-2y df/dz= -2z

Q: Find the maximum rate of change of the following function at the given point. f(x, y, z) = x² + 5xz…

A: To Determine: find the maximum rate of change of the following function at the given point . Given:…

Q: 2) Find the maximum rate of change of f at the given point P and the direction in which it occurs.…

A:

Q: Find the rate of change of w with respect to f at i = 1 by using the chain rule. You can check your…

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Q: Find the direction at which the function f(x, y, z) = x In(e' – xz) increases fastest at (-2, 0, 0)…

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Q: (1) Use the Chain Rule to find dz/dt. (a) z = r² + y² + xy, r= sint, y = e'. z = x2 +y?, x = cost+…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the maximum rate of change of the the function 80 f(x, y, z) = 1+g² + 2y? + 3z² %3D at the…

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Q: Let f(x, y) = xe*Y. Find the maximum rate of change of f at the point (2, 1). хе

A: We will find the maximum rate of change.

Q: A particle moves in a plane according to -t, x = (t+1)e; y=2tet -t Determine the simplified…

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Q: Find the direction at which the function f(x, y, z) increases fastest at (2, 0, 0) = x In(e' – xz)…

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Q: Find in what directions does flx, y, z) = 4x 2– 9z + 2z In(y) increase and decrease most rapidly at…

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Q: dz If z = e2x+ 3y and x = In t, y = t2, calculate from the total dt derivative formula and show that…

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Q: Let f (x,y,z) = xln(yz). Find the maximum rate of change of f at the point (1,2,;) and the direction…

A: Suppose f  is multivariable function as f=fx,y,z then gradient vector is a vector that is composed…

Q: 8. The temperature of the xy-plane is given by the function f(x, y) = x²y+e¬¤. (a) At the point…

A: The direction of maximum decrease of a scalar function f(x, y) is given by the negative of the…

Q: Find the linear approximation of the given function at (0, 0). f(x,y) = sqrt(y+(cos(x))^2)

A: The given function fx, y=y+cos2x The linear approximation in 2 variables is given by Lx, y-fa,…

Q: Let f(x, y, z) = x² + 2y+ e³=2« + 2°. Find the rate at which f is changing at (1,2, –1) in the…

A: Use the formula of the directional derivative and simplify.

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: Given function and the point are

Q: 2. Consider the following function F (r, y, z) = x² + 2xyz + y² In z and the point P = (2,1, 1) and…

A: *The given function is, F(x,y,z)=x2+2xyz+y2×lnz *The point P is P=(2,1,1) *The vector u is u=i+2j-2k…

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

A:

Q: Suppose that the temperature in a given region is given by T(x,y)=200xy(1-x2-2y2) . Suppose that you…

A: Given that,Temperature in a given region is given byTx, y=200xy1-x2-2y2You and your friend are at…

Q: (2) Evaluate the rate of change of i with respect to t when i 15t sin 3t and t=0.1. 2e" sin 2t when…

A: Calculation of rate of change of z with respect to t is given.

Q: Find the direction at which the function f(x, y, z) = x In(e – xz) increases fastest at (-2, 0, 0)

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 2. Find (a) the gradient of f at P and (b) the rate of change of the function value in the direction…

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Q: Let f(x, y) = xe". What is the maximum rate of change of f at the point (2,0)?

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Q: 4x 28. If R = and errors in x, y, z be 0-001. Show that the maximum relative error at x = y = z = 1…

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Q: 3. Evaluate the gradient of S(1, y, 2) = In(cosh z+ y) - arctan| at (1,y) = (7/2, 1).

A: Given that fx,y,z=lncosh x+y-z2 arctanx2y2+z2 To find the gradient of f(x,y,z) :…

Q: Find the linear approximation of the function y = x' at point xo 1 О а. у %3D Зх — 2 -

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: We have to solve

Q: #2. Consider the function f (x, y,z) = xy+3xz² + 5y at the point (1,0, 2) (a) Find the direction in…

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Q: Consider the following function F (x, y, z) = x² + 2xyz + y² In z and the point P = (2,1, 1) and…

A: Consider the function, point and the direction  F(x,y,z)=x2+2xyz+y2lnzP=2,1,1u=i+2j−2k

Q: Find the direction in which the function f (x, y, z) = xy - In z is increasing most rapidly at the…

A: We will use directional derivative here

Q: 4. Find (a) the gradient of f at P and (b) the rate of change of the function value in the direction…

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Q: 35. Find all points at which the direction of greatest rate of change of the function f (x, y) = x²…

A: Find your answer below