1. Sket dh the graph of the cylinder r = (y – 2)2 in R. %3D

Q: Use an iterated integral to find the area of the region. dy dx = y 81 7 5 4 3 2 1- 1 2 3 4 6 8

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

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Q: Find the conservative vector field for the potential function by finding its gradient. h(x, y, z) =…

A: We have to find the conservative vector field.

Q: Evaluate the iterated integral. x dz dy dx 128/15 16/89 23/6 6.

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

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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: Evaluate I| xy dA where R is the region in y = x2 A) 13/7 B) 16/3 18 D) 20

A: We have to evaluate the integral.

Q: 13.3 PARTIAL DERIVATIVES 29-32 Evaluate the indicated partial derivatives. I 29. f(x, y) = 9 – x² –…

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Q: Evaluate the double integral over the rectangular region R. | 8xy'dA; R = {(x, y): -1<xs 1, - 8 syS…

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

Q: Evaluate JJ xy dA, where R is the region in (1, 3) (5, 3) R (2, 1) (4, 1) A) 56 В) 67 с) 38 90

A: Explanation of the answer is as follows

Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere X + y +…

A: Here, to find the volume if the solid enclosed by: x2+y2+z2=4a2 The cartesian to spherical…

Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 5x2y²j

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Q: Fidn the sum: 2k (Write your final answer in fraction form, when applicable) A=31

A: Use the formula of summation then put the limits .

Q: Sketch the region enclosed by the curves and find its area. cos 5x, y = 0, x = x = 10' 5 NOTE: Enter…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

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

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1.

A: The given integral is ∫c(x+3y2)dy   and the curve C is x=2t,  y= 6t   where 0≤t≤1 Now, y=6t⇒dy =…

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

A: Given

Q: Question 2 Use double integration to find the volume of the solid bounded by the paraboloid z = 9x2…

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Q: Evaluate (2x – y) dx + (x + 6y) dy. C: x-axis from x = 0 to x = 9

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Q: Directions: Evaluate the derivatives of the following functions with respect to x and simplify the…

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Q: cos (0 + 11) y = Use symbolic notation and fractions where needed.) dy -4 cos (0+11) sin(0+11)| do

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Q: Find div F and curl F if F(x, y, z) = xz*i+ 6y°x*j+4z²yk. %3D div F= curl F=

A: To find the divergence and curl.

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

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Q: r = V cos 20 r = 5 cos 0

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Q: Find the center of mass of the given system of point masses lying on the x-axis. m = 8, m, = 3, m, =…

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Q: (c) Sketch a graph of the path, and sketch the velocity and acceleration vectors at the given point.…

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Q: For each of the following series determine if the series converges or diverges. 00 In(n) Σ n n=2 n3…

A: The given series,1. ∑n=2∞ln(n)n2. ∑n=0∞n3n4+1

Q: first octant 2 4- x+y dy dx -

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Q: Evaluate JJ Xy dA, where R is the region in LA ... y = x? R 2 A) 13/7 B) 16/3 c) 18 D) 20

A: A detailed solution is given below

Q: Question 13 2 Evaluate the iterated integral. yz dx dz dy

A: Evaluate the iterated integral .

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction to PQ

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Q: Current Attempt in Progress Find the area of the region inside the circle r = 18 sin 0 and outside…

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Q: Question 16 Use double integration to find the volume of the solid bounded by the paraboloid z = 9x…

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Q: Find the length of the curve, L. y? = 64 (x + 5)* , 0 0

A: The solution is given in the next step.

Q: The integrand of the definite integral is a difference of two functions. Sketch the graph of each…

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Q: Question 2 Use spherical coordinates to find the volume of the solid. The solid enclosed by the…

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy : -54 -36

A: Triple integral

Q: 'ind the area of the region that is enclosed by the cardiod = 20 + 20 sin 0. OTE: Enter the exact…

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Q: Find the area of the region enclosed by x² and y integrating with respect to y. the curves Y = 4x by…

A: A detailed solution is given below

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: n-1 1. b) Determine whether the series is convergent or divergent. If it's convergent, 4" n=1 find…

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Q: Find the exact arc length of the curve over the stated interval. 1 1 Gy, from y =1 to y = 3 12 NOTE:…

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Q: Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the…

A: We need to set up and evaluate integral.

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. p…

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Q: Evaluate the integral by choosing a convenient order of integration: x cos(xy) cos' (Tx) dA; R 0, x…

A: Given

Q: 1- sine Evaluate the iterated integrals J. J. r2 cose dr de̟ A ) 1 В 2 (c) o D 3

A: The integration of the double integral is r2Cos(theta).

Q: V4-x² c 3-x2-y² Evaluate the iterated integral. x dz dy dx -5+x²+y² A 128/15 в) 16/89 c) 23/6 6.

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A: Directional derivative: D f = del f • unit vector of direction

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

A: Given data÷