Work done by the force F(x,y) = (3x² +3e-7+(-4y²-3xe - acting along the curve y = x³ for 0≤x≤l is equal to: O 0.35880499018099377 O 1.1917049901809937 O 0.77030499018099374 O 0.98260499018099368 O0.5590049901809937

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A: Given: f(a)n=1 if n=0nan-1 if n≠0and f(b)n=bn To find: b2010=?

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Q: Work done by the force F(x,y) = (2x² +2e +(-3y²-2xe acting along the curve y = x³ for 0≤x≤l is equal…

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A: We can solve this problem using partial derivatives.

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Q: Find of z = In(xy)

A: Given,Z=ln(xy)differentiating both the sides partially w.r.t. x∂z∂x=1xyy1∂z∂x=1xagain differntiating…

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Q: Find div F if F(x, y, z) = (x2 + y) i + z2 j + (ey - z) k.           A . 2xy i + k          B. 2x…

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Q: Evaluate SIL. dydzdke, where E = {(x,y,z): (2+z12<x< 2, - (4 - z)2sy <(4 -2)12, 3<z 58}.

A: Given: The given integral is ∫∫∫Rdydzdx The given intervals are (y2+x2)12≤x≤2, -(4-z2)12≤y≤(4-z2)12,…

Q: Sv.Vdxdy = dxdy = ду 2 + JR V.(6,x)-V,(b,x)]áx + [ [7 (a, y) –V,(0,v)ky.

A: Here is the solution of the given problem.

Q: Real mathematical analysis proof : If x, y are non-negative real numbers, prove that x + y = y + x…

A: We have x, and y are non-negative real numbers. We have to prove that x+y=y+x and x·y=y·x.

Q: Evaluate fv*+1dx x2 A. 를 (1 +즐)를 -를 (1+ 즐)를 :. 를 (1-즐)를 -를 (1-2)를 + C + C + C D. + C Evaluate the…

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Q: for z = In(2® + y*). Find

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Q: prove that ਰ Apply the calculus of residues to dx (1 + x²)² - π 4 .

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A: Given ∫F→dr→=∫x+4y2dx+x2ydy

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Q: Let Find A = x³y 1-2xz] + 2yz k Vx(VxA).

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Q: Q.5: Derive reduction formula of f cot"x dx. Also prove that -cot*x cot2x S cotx dx = + InSinx + C.…

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A: Here we have to draw the graph of the function.

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Q: If u = 2-x, x/2-xd

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Q: 1-ス 17+4 キ文T AND FIMD

A: Given that:x=t+t-1 and y=t2+t-2

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Q: f ▼ is defined by V= d/dx i + d/dy j + d/dz k and A& functions then show that V.(A+B)= V…

A: ∇=ddxi+ddyj+ddzkA and B are differentiable function then ∇.A+B=∇.A+∇.B

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Q: aF O F2 aF, If F = F,I+Fj +F,k then prove that div F = + ду

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Q: Determine the vesulting equaton Determine the vesulting equaton after using the suitable…

A: We have to find

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Q: ôw ôw + = 0 for w = Ax, y), x = u – v, and y = v – u and demonstrate the ди ду 6. Show that result…

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Q: Let f(x, y, z)= and c(t) = (t, 13/2, t). Compute ff ds y+z

A: The given function is fx,y,z=x+yy+z, and the curve is given by c(t)=t,23t3/2,t. To Evaluate:…