Evaluate (2x – y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (2, -7)

Q: Find the area of the region inside the circle r = 12 sin 0 and outside the cardioid r = 4+4 sin 0.…

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Q: Find the centroid of the region. NOTE: Enter the exact answers. (¤, g) = |(?, ?) %3D y = =? 1

A: y=x7

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) stk lim (ei + Sin(/)j + e…

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Q: Find the principal unit normal vectóř tô thể curve at the r(t) = /2ti + e'j + e-k, t = 0 %3D

A: Principal unit normal vector

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Q: r2 cose dr de valuate the iterated integrals A) 1

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Q: Find V x (V × F) if F(x, y, z) = 4xyj+ 9xyz k. V x (V × F)

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Q: 27х3-8а3 y3= y= 3x-2a Зх-2а

A: Y'=?

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 5…

A: To evaluate: ∮C5y2dx+5x2dy Let, L=5y2& M=5x2⇒∂L∂y=10y, ∂M∂x=10x

Q: 59-64 Use Property 8 of integrals to estimate the value of the integral. x'dx 60. | Jo x+4 59. dx…

A: ∫xn dx = xn+1n+1 +C ∫tan x dx =ln sec x+C

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A: We have to find the volume of the solid.

Q: Evaluate the triple integral. /I| ry sin(yz) dV, G where G is the rectangular box defined by the…

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Q: ローペープ 8-x²-y z?dzdxdy. Use cylindrical or spherical coordinates to evaluate the integral.

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Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy -162 -108

A: ∫02∫-162y2∫-108zyz dx dz dy∫-108zyz dx=(xyz)-108z…

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Q: lim 48V x 487Y

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Q: Consider the following algebraic functions. F(x) = -x2 + 6x + 5 g(x) = x+ 5 Sketch and shade the…

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Q: Represent the plane curve by a vector-valued function

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Q: Find the volume of the solid that results when the region enclosed by the given curves is resolved…

A: Solution is done in step 2

Q: Evaluate the integral / (2x + 3y)dx + (6x – y)dy along the parabolic arc y = x' from (0,0) to (1,1).…

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Q: xe*y dy dx

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Q: Determine the surface area of the solid obtained by rotating y=v9-x from -2sxs2 about the x -axis.

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Q: Evaluate the iterated integral. IT (10 + 2x2 + oy?) dx dy

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Q: Find div F and curl F if F(x, y, z) = 10e"Y i – cos yj+ 8 sin? z k. div F= curl F=

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x3 - y3, P(4,…

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Q: (1 point) Use the Divergence Theorem to calculate the flux of the vector fields F, = -Szi + 5xk and…

A: Find your answer below

Q: Express the area of the given surface as an iterated double integral, and then find the surface…

A: We have to find the surface area.

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A: Vector equation of a line passing through P(a,b,c), Q(p,q,r) is given by,…

Q: NC2)=

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Q: Find the unit tangent vector to the curve at t r(t) = t°i + 3t?j, t= 2 T(2) =

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Q: Determine the work done by the constant force. The locomotive of a freight train pulls its cars with…

A: Given data÷

Q: Use double integration to find the volume of the solid. ... 3x + 2y + 4z = 12

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Q: the first quadrant bounded by the graphs of y = V16 – x², y = 0, andx = 0 is revolved about (a) the…

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Q: Find V (V x F) if F(x, y, z) = 5 sin xi + 9 cos(x – 2y)j+ zk. V. (V × F) =

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Q: Express the iterated integral as an equivalent integral with the order of integration reversed.…

A: Express the iterated integral as an equivalent integral with the order of integration reversed.

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) 6t + sin(8t) i + e-4°k lim…

A: To find the limit of the given vector function.

Q: n? +1 2. Determine whether the series is convergent or divergent. If it's 2n² +1 n=1 convergent,…

A: The given series,        ∑n=1∞n2+12n2+1

Q: What is the volume of the largest cone having its circular base circumscribed about a face of a…

A: To determine the volume of the largest cone having its circular base circumscribed about a face of a…

Q: If f is continuous at a number, x, then f is differentiable at x. True False

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Q: Question 20 Evaluate JJ xy dA , where R is the region in y = x? R (A) 13/7 (в) 16/3 18 D) 20 2.

A: We have to find the area.

Q: 1. Determine whether the series is convergent or divergent. If it's n=l e"+1 convergent, find its…

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Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) dx…

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Q: Find div F and curl F if F(x, y, z) = 13y*z'i – 11a'2®j – 5xy*k. div F= curl F=

A: We can solve as follows

Q: d Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating d dt dt the product directly…

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Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A: Given points,  P(0,0,0), Q(4,2,4)

Q: Find V. (V × F), if F(x, y, z) = e²i+ 3xe"j – 7ev*k. - V · (V × F)

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Q: 5² - 13 ニ

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Q: Find the area of the region(s) enclosed by the curve f(x) = x°, the x-axis, and the lines x =-1 and…

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