We are given the function f(x,y)=sin(3x+2πy)+exy-π, and points A(π, 1), B(π + 1, 0). Find the rate of change of f at A along the direction from A to B.

Q: If z = xy + 3xy', where x = sin 2t and y = cos t, find dz/dt when t = 0.

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Q: z = e*sin y, Mo (1,2) 6

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Q: The approximation of I = xe" dx using Simple Simpson's rule is:

A: According to the fundamental theorem of calculus ∫abf(x)dx=F(b)-F(a), where dFdx=f(x). Simpson's…

Q: Find the derivative of the function h (x, y, z) = cos xy+ e+ In zx %3D at P. (1, 0, 1/2), in the…

A: Here we have to find directional derivative of h(x,y,z) in the direction of u.

Q: The linear approximation at r = 0 to sin(2x) is A+ Bx where A is: and where B is:

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Q: Find the differential of the function f(x,y)=x(e^-y) at (2,0). df=?

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = V4 - x2 dy =

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Q: The linear approximation at z = 0 to sin(8x) is A + Bx where A is: %3D and where Bis:

A: Given : The linear approximation at x=0 to sin(8x) is Ax + B   To Find : Value of A and B

Q: If f(x) = xe , x >0 and (Y = ln(X)), then the PDF of Y is %3D (In(1)² (In(y))e ye

A: Answer: ⊙ ey-12e2y

Q: Find dw/ dt at t = 0 if w = sin (xy + p), x = et, and y = ln (t + 1).

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Q: Let y = tan(5z + 6). Find the differential dy when a = 4 and dæ 0.1 %3D Find the differential dy…

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Q: Compute /. x² dx dy dz, where E = {(x, y, z) : x² + y² < 1,0 < z < 1}.

A: To evaluate ∬∫Ex2dxdydz, Where E is the region E=x,y,z:x2+y2≤1, 0≤z≤1.

Q: If f(x, y) = 4x? – 8y, then the total differential of f at a = 1 and y = -2 is : O df = 8 dx – 32 dy…

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Q: The linear approximation at x = 0 to sin(9x) is A + Bx where A is: and where B is:

A: Given fx=sin9x Differentiate fx=sin9x with respect to x, we get f'x=ddxsin9x=9cos9x Hence,…

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 total differential of the function. 4y f(x, y) 5x - y df =|

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Q: Let y = f(x), where %3D 7 f(x) = x + Find the differential of the function. dy =

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Q: use the chain rule to find dz/dt, where z=x sin y, x=t^5, and y=5t^2 please show steps

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Q: COS f(2, Y) af af dy f(x, y) = log, (3x) af %3D fe dy

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Q: The linear approximation at z = 0 to sin(4z) is A+ Bz where A is: and where B is:

A: Linear approximation is found by L(x)=f(x)+f'(x)(x-a) Differentiate L(x) with respect to x.…

Q: dz Find dt if z = x²y – sin y, x = vt? +1 and y = e -

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Q: Use the differential dz to approximate the change in the function z (shown in the image) as (x, y)…

A: Given that:   The given function z = f (x, y) moves from the point (1, 1) to the point (1.03, 0.95),…

Q: The linear approximation at x = 0 to sin(2x) is A + Bx where A is: and where B is:

A:

Q: The derivative of f(x,y)=9xY at (e,1) in the direction of v=(4,3) is !!

A: TO FIND THE DERIVATIVE i.e DIRECTIONAL DERIVATIVE IN DIRECTION OF V= (4,3) at (e,1) STEPS 1. FIRST…

Q: The linear approximation at a = O to sin(7x) is A + Bx where A is: and where B is:

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Q: Find the average velocity of the function over the given interval. 2) h(t) = sin (3t), |0, D) A) B)

A: The given function is h(t)=sin (3t), 0,π6 We have to find the average velocity of the given function…

Q: Suppose that the position of a body moving along a coordinate line at time t is a. s = a cos kt + b…

A: Part (a):Part (a):Given,Given,

Q: В. Find dz/dx , əz/@y at the point (1,1,1) if x³ + z2 + ye*z + xz cos y = 0 .

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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 total differential dw. 4. w = e*" – sin(yz) -

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Q: Find the differential of the function w = x* sin(y z' ) dw dx+ dy+ dz %3|

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Q: Assume that x and y are both differentiable functions of t and are related to the equation: y =…

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Q: Use the Chain Rule to find dz/dt. z = x2 + y?, x = cost + sin t, y = cos t – sin t. -

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Q: Find the differential of the function. Z = e cos(2nt) dz = dx + dt

A: Given,

Q: Find the value(s) of dx at y=1 given that x²y+ y² = 5.

A: Given,        x2y+y2=5  and dydx at y=1

Q: dz Use the Chain Rule to find dt for z = x? + y? + xy, x = sin t, y = et.

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Q: Determine the numerical value of dF of the function F(x, y) = e-3y cos(nx) given that X = 1, y =…

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Q: Find the linear approximation to h(y)=sin(y+1) at y=0. Use the linear approximation to approximate…

A: Linear measurement is one-dimensional. A linear differential equation is an equation where the…

Q: The linear approximation at x = 0 to sin(4x) is A + Bx where A is: and where B is:

A:

Q: When reduced to a linear DE of order one in z, the Bernoulli's equation +y)=3x<y becomes dx dz 1 A…

A: Topic  =Differential equation Correct option  = A

Q: Find the equation of the tangent plane to z = ln(2x + y) at −1,3

A: Find the equation of the tangent plane to z = ln(2x + y) at −1,3

Q: Find the differential of f(x, y) = vx2 + y³ at the point (1,2). df

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Q: Find the directiona derivative of f (x, y) = In(e* – 4y at the point (0, 0) %3D - in the direction…

A: We have to solve

Q: Verify the linear approximation at ( 0, 0) for e^x cos(xy)

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Q: Find the total differential df to the function f(x, y) = x²y – xy? when x decreases from -2 to -2.01…

A: We will find out the required value.

Q: Find the differential of the function f(r, y) = ye" at (0,-1). df =

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Q: (b) Calculate the rate of change of the function f(r, y, 2) = ryz along the path r(t) = (sin(t), e“…

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Q: Use the Chain Rule to find dz/dt. z = sin(x) cos(y),    x = The Square Root of t,    y = 8/t

A: Given: z = sin(x) cos(y),    x = √t,    y = 8/t By Chain Rule,