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.

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

A: topic - derivative of a function

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

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Q: (i) Integrate the following functions with respect to x: 7 y =- 4x 2x - 3 y = 2 y = x* sin (x° +1)

A: Explanation of the answer is as follows

Q: hi, i've added the problem as a picture please take a look. thanks in advance!

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Q: f(x.y) =e^sin(y) + In(xy) ; әз of Әхд-у

A: Given: fx,y=exsiny+lnxy To find the partial derivative of ∂3f∂x∂2y Partial differentiation: Partial…

Q: evaluated at x = 0.001 and y = 0.002 Compute the derivative of the following: 5 g(x) =, 2.1'x f(x) =…

A: topic - derivative of a function

Q: Let y = f(x), where f(x) = 5x² + 5. Find the differential of the function. dy = X

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Q: (b) If z= 3x² + y² 4xy Hence, Show that find ôz dz dx dy Ox 3 3x a²z y a²z y ổr x ô and =0 8² z 2…

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Q: If sin(x) f(x)= 68+t2 dt Jtan(x) and g(y)= f(x) dx , Then g) is equal to

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Q: Using u = 1 + t°, the limits of integration will change from t = 0 to u = and from t = 1 to u =

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Q: Suppose y = V 2x + 1, where x and y are functions of t. (a) If dx/dt = 15, find dy/dt when x = 4. dy…

A: Consider  y=2x+1 where x and y are function of t.

Q: Let y = f(x), where f(x) = 7x³ + 3x. Find the differential of the function. dy = X

A: The differential of y is the derivative of the function times the differential of x,

Q: Find the particular antiderivative of the function f(x) point (0, –1). e" (2ª – 1) whose graph…

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Q: Verify that [(y- 2x \dx +(2xy +x*dy = [S -川- dA where C is the bounda ôy R defined by y = 0, x = 1,…

A: See the details solution in below

Q: B. If R = xyz’i+÷j – yz*k_find of the differential R, dR.

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Q: 3. Is the expression (ez+y+z +4x²y²2²)dx+(e²+y+z +r’yz²)dy+(e²+y+z+³y²z)dz = 0 %3D exact? If yes,…

A: Given expression is ex+y+z+4x2y2z2dx+ex+y+z+83x3yz2dy+ex+y+z+83x3y2zdz=0 To verify whether the above…

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: Suppose that u and v are differentiable at x = 2 and that u(2) = 4, v(2) = -9, u'(2) = 5, and v'(2)…

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Q: Q4/ 2x 1- If z = f(x,y) and z = x²y³ + + 1. Determine the total differential. -"/2 2- Evaluate: 2 S*…

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Q: Given the function f(x,y) cos 2xーx3eY +āyン COS find te second partial olerivative fxy.

A: Let f(x,y) is the given function.Then  fx is the derivative of f with respect to x taking y as a…

Q: dz is equal to .. dt Let z= In (x2+y²) where x=ue"sin t and y = ue"cos t. If u= -2 and t=0 then -

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Q: If f(x, y) = y cos(x) – x* In(y), find the second partial derivative (A dx? -y? cos(x) – 6x In(y) d…

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Q: If x =0.71 and y = 0.67, then value of C in the xsin-(x) V1-x² antiderivative of F(x) = is

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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: 10) For y=v+8, use the differential dy to approximate Ay when x changes from r=1 to x=0,97

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Q: 6. Suppose that w = x cos(yz²), where x = sin t, y = t² and z = 2e'. Find the rate of change of w…

A: Using derivative

Q: If f(x, y) = 4x² – 6y², then the total differential of f at x = 1 and y = -2 is : O df = 24 dx + 8…

A: df=dx+dy (see step 2).

Q: Let y = f(x), where f(x) = 6x2 + 3. Find the differential of the function. dy =

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Q: dz at t = dt if z = f(x, y) = x² – 3xy+ 2y², x = x(t) = 3 sin 2t, y = y(t) = 4 cos 2t. Use chain…

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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: 1. Find the total derivative dz/dy, given (a) z= f(x, y) = 5x + xy – y², where x = 9(y) = 3 y2 (b)…

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Q: Q4/ Find the value of the following partial derivative (choose O 1- If w(x, y) = Ln(ey+/5xy)),find…

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Q: of Let f (x,y)=tanh-1(x-y) with x=e" and y= usinh (t). Then the value of evaluated at the point dt…

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Q: Q5. If W = x² y + 2xyz , x = t², y = t + 1, z = 2t at t = 1. Find the total differential

A: Let's find.

Q: Suppose that y is a differentiable function of x and w = sin(y2). Express the derivative of w with…

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Q: Let y = f(x), where f(x) = 3x+6/x+6 Find the differential of the function. dy =?

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Q: I the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², Find : dz dz and 2- (by chain rule)…

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

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Q: ) L(3.98) where L(x) is the linearization of y = √√x +3 at x = 1 (tangent line approximation)

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Q: 3. Find dy where; (x+y) =2 o) cos(xy)- 주+ ers + b) e+ u= xlax (use chain rule)

A: We have to find the derivative

Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

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Q: If f(x, y) = 3x? – by, then the total differential of f at x = 1 and y = -2 is : O df = 24 dx – 6 dy…

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Q: The derivative of y with respect to a given ¹ = 1 is Oy' = yx²-¹ O y'= 0 Onone of the choices Oy' =…

A: I have stated the used formula in the solution.

Q: it x and y are both differentiable functions of t and find the required = 2 (x² – 3r) Find dy/dt…

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Q: 1) Find dy for each OF Following functions du a) y = cosh (2n) + 4 ny cosh (1an 2) + 2y = e * %3D F)…

A: Product rule of differentiation:   Chain rule of differentiation:

Q: In solving the antiderivative of f(x)= 3sin(x) + 4cos(x) +5 by miscellaneous substitution, the…

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Q: Let y=3x^2  Find the change in y, Δy when x=5 and Δx=0.1    Find the differential dy when x=5 and…

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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: Suppose x, y, and z are positive functions of t. If z x + y?, dx/dt 1, and dy/dt 2, find dz/dt when…

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.