Integrate f(x, y) =x+y (4, 0) to (0, 4) over the curve C:x +y 16 in the first quadrant from %3D 32 b) 16 24 40 8.

Q: Find fr and fy- ray f(r, v) = [" 3e 3e" dt f„(x, y) = fy(x, y)

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Q: dy If y = (t + 6t + 4) (3t2 + 4), find dt dy %3D dt

A: it is required to find the derivative.

Q: Integrate f(x,y) = x + y over the curve C: x2 + y? = 9 in the first quadrant from (3,0) to (0,3).

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Q: Consider w = x² – y², where x = s cost and y = ssin t. Find u and hu using the Cha dw at ds Rule.

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Q: 2x + 7x +3. If Ax = 0.3 at x = 4, use linear Let y approximation to estimate Ay %3D %3D %3D Ay =

A: Given y=2x2+7x+3 if ∆x=0.3 at x=4 we have to approximate ∆y using linear approximation.

Q: Compute DF(, ) of F(1, y) = (e" cos(ry), r² + y) %3D

A: Given function is F(x,y)=eycos(xy), x2+y Let  f1(x, y)=eycos(xy)f2(x, y)=x2+y

Q: dz dz Calcula y dy z = x In(y) az = In(y) 1

A: Given : z = x ln( y ) To Find : ∂z∂x, ∂z∂ywe have given four options to determine the correct option…

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: Where f(x, y) y calculate (–1, 1) towards the point dv (-1, 3)

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Q: dy If y = (t + 2t + 8) (6t² + 6), find %3D dt dy dt

A: The given question can be solved as shown in step2.

Q: 2, 0 1

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Q: integrate ƒ over the given curve. ƒ(x, y) = x3>y, C: y = x2/2, 0 <=x<= 2.

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Q: ƏF Find at (x, y) = (T, 1) if f (x,y) = cos vt dt. cos yt dt. ww

A: given,          fx,y=∫0x2ycostdt

Q: Differentiate: y(x) along the curve xy =ex Show all working out.

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Q: Compute dy/dx using chain rule where y = (u^2+2u)/(u+1) and u = x(x + 1)

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Q: = Lasin(t") dt y%3D

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Q: Find dy/dt of y = Ssin (cost) and simpli -t -cos t cos t V1-? the

A: Given:- y=sin(cos-1(t))  To find:- y'

Q: valuate S S Se(3 – 4x)dV, whe e xy-plane defined by 0 < x s

A: To find: ∫∫∫E(3-4x) dV

Q: Let y = 3x + 3x + 2. If Aa = 0.4 at x = 1, use linear approximation to estimate Ay | Ay a

A: We have to find the change in y using linear approximation

Q: = y – 2², dt dy = y - ar. - у — dt For parameter a, classify the equilibrium points when a>5

A: Both the equilibrium points (0, 0) and (a, a2) are saddles.   Explanation: Let   First, we find the…

Q: Compute 6. da dy dz x²+y² + z² where V = {(x, y, z) E R³ : 4 0, y > 0}. Sketch the solid.

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Q: Find the work done by F(x, y) = (x, Y) over the curve r(t) = (e' cost, e' sin t) (x² + y?)3/2 from…

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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: b- dy +2y=0; y=1 at t=0, y(0)=1 dt

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Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A: Let the required path be γt=xti+ytj . Then the velocity vector in the direction of maximum…

Q: Integrate f(x, y) = (x + y + 1)- 2 over the triangle with vertices (0, 0), (4 , 0), and (0, 8).

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find dy or y' using implicit differentiation. r'y-y= Oy 1- 3r'y %3D Oy = 1 3z'y 3z'3y 1 %3D 1 3z'y…

A: The given equation is x3y3-y=x

Q: d²y dr +24 -52y=0; y(0)=; v'(0)= ; y'(0): dt Use Rod.uction ofE Ordor 3

A: Explanation of the solution is given below....

Q: Integrate f(x,y) = x-5y over the curve C: x +y = 64 in the first quadrant from (0,8) to (V32,/32).…

A: Formula Used:Line integral ∫Cf(x, y) ds=∫abf(x(t), y(t)) dxdt2+dydt2dt

Q: Find the length of the curve y = V cos 2t dt from x= 0 to x = 4

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Q: Find the moment of inertia with respect to x-axis the aarea bounded by 2y^2-8y-16x=0 and the line…

A: The moment of inertia is the rotational analogue of mass. The expression for moment of inertia is…

Q: Integrate f(x,y) =x -y over the curve C: x² + y = 16 in the first quadrant from (0,4) to (V8,18 - y)…

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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: Integrate h (x. y.2) = yzi+xj+xzk over the indicated path: the line segment from (0. 0. 0) to (1. 1,…

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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: z = √xy, dz dt t², y = -t² then 2 2 2t²) =?

A: We have to choose the correct option from the given options according to the given information

Q: Integrate f(x,y,z) = x-3y + z over the line segment joining the points (0,0,0) and (2,2,2). %3D

A: Here, we need to integrate f(x, y, z)=x-3y2+z over the line segment joining the points (0, 0, 0) to…

Q: (a) Calculate the line integral (4x+2y²)dy where C' is the curve y = 2³, starting from z = 0, y = 0,…

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Q: he The product of linear integration is where c t $ (2xy – x²) dx + (x + y²)dy, x = y? 30 y = x? ,…

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Q: Y" - Y = { 2, %3D Ost Y(0) = Y'(0) = 0, %3D %3D t21

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Q: Let y 4x + 3x + 4. If Ax 0.3 at a = 3, use linear approximation to estimate A %3D Ay =

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Q: Integrate f(x,y) =x+y over the curve C: x² + y = 49 in the first quadrant from (7,0) to (0,7).

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Q: . Use fourth order Runga Kutta Method to find y at x=0.1, given that dy = 3e* + 2y , y(0) = 0 and h…

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Q: a. Apply the Runge-Kutta method of 4th order to find the approximate value of y for x =0.2, dy in…

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Q: Use the Chain Rule to find dQ where Q=√√3x² + 3y² + 4z², x= sint, y = cost, and z= cost. dt'

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Q: Compute ∫C y dx + xy dy if C goes from (0, 0) to (1, 2) along the line parameterized as x = t, y =…

A: Here I am attaching image so that you understand each and every step.

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: Compute on your paper, showing all work: dy dx (i) = x + y (ii) y = xy + 2x² at the point (-1, 1)…

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Q: dz dt || z = cos(x + 3y), x = 8t³, y = 9/t

A: By the use of chain rule we need to find the required derivative.