Find V (V x F) if F(x, y, z) = 8 sin xi + 6 cos(2.x - 3y)j + 7zk. %3D | V. (V x F) =

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A: Write the nth term and  add them to get Sn .

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A: ∫0π/2 cos9tdt ∫0π/2 cost(1-sin2t )4dt here lets substitute that sint = u du/dt = cost du = costdt…

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Q: Q2) Find the integral of: f*,6 tan*x dx

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Q: Find the series radius and interval of convergence for what values of x does the series converge x"…

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Q: Find the volumes oF the solids geverated by revolving +he regions bounded by the graphs oF the…

A: Given:-  the region bounded by  y=2x2y=0  and x=2rotating about the x-axisusing washer/disk method…

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Q: 1 3. Savads 4Vūdu 4.

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Q: roduct directly and then by applying the formulas dr dr r(t) and dt dr, dr x ). dt Fi(t) - cos(t)i +…

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Q: Find r'(t). r(t) = (tan-(11t))i+t cos(t)j – Vik

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Q: e- + cos (xy) = (4 – 3z) (2 + 2.x), UIM 4. find ду ÚTM az cos (ху) — (4 — 32) (2- 8 UTM UT UTM

A: Partially Differentiate with respect to y

Q: Find div F and curl F if F(x, y, z) = 17y*z4i – 3x°z®j – 3xy°k. - div F= curl F=

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Q: Describe the graph of the equation. r= -3 i+tj+(t2-1) k O Itis a parabola in the x = 3 plane, vertex…

A: This is a problem related to parametric equation plotter. Based on the x, y and z value in terms of…

Q: 3. Use chain rule to find given w = Vx2 +2y2 + z² and a cos (st), y = -2s In t ane 2 = 3s?Vt. 3s2Vt.

A: Follow the procedure given below.

Q: Find [r(t) · u(t)] and [r(t) × u(t)] in two different ways. dt dt r(t) = ti + 8t2j + t³k, _u(t) =…

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Q: ||r'(t) x r"(t)|| Use the formula k(t) to find k(t). 13 ||M(t)||* 15: r(t) = t’i + tl5j K(t) =

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Q: Evaluate the definite integral. 1+eJ+/k]di i-ej+ k o ? - 1 1 + (-" – 1) j + k e-1)1- (e - 1) J+ k o…

A: Given: I=∫01e9ti+e-tj+tkdt As we know that; The Power rule: ∫xndx=xn+1n+1+C And ∫eax+bdx=1aeax+b+C

Q: Find div F and curl F if F(x, y, z) = 16y°z³i – 9x°z°j – 7xy'k. - - div F= curl F=

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Q: Question 5 Consider the exact first order diff. equ: M(x, y) = 2.xy –3x? N(x, y) = x² - 2y (I):…

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A: We have to find the area of the shaded region.

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Q: Find V x (V x F) if F(x, y, z) = 2:xy j+ 9xyz k. V x (V × F)

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Q: 5. This problem will walk you through using integration to find the formula for an area of a circle:…

A: equation of circle  x^2+y^2=1 y^2=1-x^2 y=±1-x2 according to question circle lies only 1 quadrant so…

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Q: Find div F and curl F if F(x, y, 2) = 17y*z*i – 3a*2®j – 3ry®k. div F= curl F=

A: Divergence of F: ∇·F=i→∂∂x+j→∂∂y+k→∂∂z.i→17y4z4-j→3x3z6-k→3xy6 ∇·F=∂∂x17y4z4+∂∂y-3x3z6+∂∂z-3xy6…

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Q: Consider the exact first order diff. equ: M(x, y) = 2.xy – 3x² N(x, y) = x² – 2y (I): (2xy-3x )dx +…

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A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find div F and curl F if F(c, y, z) = 5y°z'i – 14x°z°j – 5xy°k. div F= curl F=

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A: This question can be solved using the concept of domain and of functions and value of a function at…

Q: Find r'(t). r(t) = (tan-'(11t))i+t cos(t)j – Vfk NOTE: Enter your answer in terms of i, j, and k.…

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Q: Match each point in polar coordinates with either A, B, C, or D on the graph. D

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Q: 3.

A: ∫x41-x2dxPerform trignometric substitutionSubstitute…