Find f'cx) a) fcx) 1. %3D +3 b) fcx)- (I+\5x)* 4

Q: Use Green's Theorem to find f. [(2x – y+ 4) dx + (5y+ 3x – 6) dy] around a triangle in the xy plane…

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Q: 2 consider, Differentiate with respect to x', dy C」.2ス %3D de

A: From the image , two find a differential equation eliminating the constants from the given relation.…

Q: Let f (x, y) = 3x2 + 2xy + 5y. (a) Calculate df/dx (1, 4). (b) Evaluate df/dy at (x, y) = (1, 4).

A: Differentiate the function f with respect to x treating y as a constant to calculate ∂f∂x.

Q: Iffis of class c? and z= f(y.x), con u= x°y°,v = 5x+1. Verify that| :4xy kxy+ 4x³y° + 10xy- af дхду…

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Q: If the substitution u = x/2 is made, the integral 1-(플)2 dx = %3D -

A: Let's integrate.

Q: Let /:R'R. S(x. y.2) = (e' tan y,x' In y). Compute D(f).

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Q: Show that the function u e(xy) + Vry V(y/x) provides the quation = 0. dy?

A: Again differentiate,

Q: Let y = 2x + 2x +3. If Ar = 0.2 at a = 2, use linear approximation to estimate Ay %3D Ay Submit…

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Q: Find af af and f(x, y) = etry In(6y) af 4yln(6y)e^(4xy) af 1/ye^(4xy)+4xIn(6y)e^4xy dy f(x, y) = cos…

A: In the first part the answer is correct but you have mistakenly not taken bracket for 1/y . You can…

Q: Use Green's theorem to evaluate Sc(y² + x³) dx +xª dy where C is the perimeter of the square [0, 1]…

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Q: 20. Show that a²F(x, y) -dx dy дх ду over the rectangle xo < x < x1, Yo < y < y1, is F(x, у) — F(x0.…

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Q: (b) u = Vt² + 2vt3 - 1 tan I (d) y = sec I VE-1 (f) y = VI+1

A: Since you have asked multiple subpart, as per our guidelines we are supposed to answer only first 3…

Q: Let z = e* sin(y+a), show that %3D ôx? oy?

A: Given, z=e-xsiny+a, then we have to show that ∂2z∂x2+∂2z∂y2=0.

Q: Numerically integrate f(x) = x2 from a=0 to b= 2 using a multiple segment (n-2) trapezoidal %3D…

A: Trapezoidal rule  ∫abf(x)dx≈Δx2​(f(x0​)+2f(x1​)+2f(x2)+2f(x3​)+⋯+2f(xn-1​)+f(xn​))whereΔx=b-an

Q: Prove that A <m AUB where AUB = {0x | r E A}U{ly|y € B}.

A: Solution: Let us consider two sets A and B. It may be possible that A∩B≠∅. But we want to construct…

Q: Evaluate S S f3zdV where E is the solid enclosed by z = 1 and z = x2 +y?

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Q: 2. Show that the function u p(ry) + Vry v(y/x) provides the equation Pu = 0. ду? dx²

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Q: of the valve matix is consistant e an linear

A: Given augmented matrix is: -412h2-6-3 Let the variables be x, y. The above augmented matrix will…

Q: Hiws slove du 4 dt %3D dx2 u(6,t) = L (8,t)=0 U(x, a) =0 : =4X-()x²

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Q: Show that y^3dx+3xy^2dy=0 is separable and exact

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Q: Evnlunte: (а) (- xy) dydx (b) dr(x-) dy, where y, = Va? - x?

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Q: Evaluate O F.dT where +(3y %3D y + 1 and C is the triangle with vertices: (0,0), (6,0), (3, 5).

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Q: B. Use Greens Theorem to evalute é yx dx + x*dy as shown bele Left Half of (0.5)

A: Introduction: Let C denote the positively oriented, smooth, and simple closed curve in a plane and D…

Q: Let f(x, y) = xcosy-y e*y. fry at (1,0)is equal to: %3D 1

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Q: (b) Apply the method of contour integration to prove that (2m de 2n Jo 2+cose 3

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Q: Calculate the LOS of y = x² + 2x + 8 LOS is x = a is b is cis

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Q: Find the Second appoximation for the System. X Sin y at (xo,,)= (1, 1). y=Cosx

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Q: Evaluate xy dx + a*dy, where C is the rectangle with vertices (0,0), (2,0), (2,1), and (0,1)

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Q: Numerically integrate y=x-X+4 from a-0 to b= 2 using single segment trapezoidal rule. O 12 0 8 0 6 O…

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Q: Consider the solid lih S,: X=4-y² そ=2

A: Surface: Surface, A two-dimensional collection of points (flat surface), a three-dimensional…

Q: Use Green's Theorem to calculate 4. [(x² – xy) dx + (y² - 2xy) dy] where C is a square with vertices…

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Q: . Show that the function u = p(ry) + Vry v(y/x) provides the quation = 0. ду? %3D dx²

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Q: Prove that (x+) ) is the rolution on the dipporen tial equation y'+ y-e 9= C,e*+ C2x + Cg, y" - 4 y"…

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Q: Show that the function u = p(xy) + VrY v(y/x) provides the uation x2 = 0. dy?

A: First find the partial derivative of the given function with  respect to x :

Q: @ Consider the DE, dx %3D dt x (2t -7) What meho can be uoed

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

Q: Integrate h (x. y) = yi+xj over the indicated path: r(u) = ui+ u²j. ue [0, 1).

A: Given hx,y=yi+xj and ru=ui+u2j, u∈0,1 We have to integrate hx,y=yi+xj along the path ru=ui+u2j…

Q: Let X - Y (3, 0.02). Given Ttx = 300 calculated by the Esscher Premium Principl %3D

A: From the given information, X~γ3, 0.02 fx=0.023γ3e-0.02xx3-1, x&gt;0       =0.000004e-0.02xx2,…

Q: dw If w = f(x, y, z) = In(x² + y? z?),x = cost y = sin t ,z = 4VE , then is : dt %3D %3D

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Q: Express x = In(3t), y = 5 – t in the form y = f(x) by eliminating the parameter. %3D y =

A: Given that x=ln(3t) and y= 5-t we need to write y=f(x) by eliminating the parameter  Now , x= ln(3t)…

Q: Let f (x,y) = sin(xy) + x² ln(y). fyx at (0,) is equal to: %3D А. 33 В. О С. 3 D. 1

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Q: 2x dV, where E is bounded by the paraboloid x = 2y2 + 2z2 and the plane x = 2. %3D

A: The given integral is ∭E2xdV. The region E is bounded by the paraboloid x=2y2+2z2 and the plane x=2.…

Q: Show that the line integral / 2re" dx + (2y – x²e¯") dy is independent of path where C is any path -…

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Q: integrate t dt/(1-ct) where c = const.

A: Solved below

Q: Show that the subtangent to y = x' at x = a is equal to a/3.

A: Definition used -                            Length of subtangent =ydxdy

Q: Assume that w=f(s° +t) dw dw and ds and f'(x) = ex. Find - dw %3D at dw ds

A: Given : w=f(s3+t2)  and f'(x)=ex