Use a double integral to find the volume under the plane z = 22x + yand over the rectangle R = {(x, y): 3 < x < 5,1 < y < 2}. i cubic units

Q: n° 3. Determine whether the sequence a, - converges or diverges. If it n – 2n° converges, find the…

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (e2i + Sin(/e) j+e-k 7t

A: Limt-0 (e2ti+sin(7t)j/(7t) +e-5tk).

Q: mparison test to determine whether the given series conve:

A: Please refer to the image below

Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y= 0, y = 7+a*…

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Q: Evaluate (z° + 6) dæ (z³+6)® +c А. 18 (z³+6)° В. +c (x³+6)* 16 С. z18 + 2x15 + c

A: topic - indefinite integral

Q: Point Func tion h(x.y)-7ycos (x-y) Co,Ti/3) Dn(o,1/3) = %3D

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Q: Find [r(t) u(t)] and [r(t) × u(t)] in two different ways. dt dt r(t) = cos ti + sin tj + tk, u(t) =…

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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: Evaluate the definite integral that represents the volume of the solid formed by revolving the…

A: Explanation of the answer is as follows

Q: 10. y = 1 11. x' +xsin y = ye" 12. In(x+ y) = tan (xy) sin

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Q: find SCE) at timet V=-5t+5, S0) = 14

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Q: r(4) (arcsin(t), arcos(1),0

A: Given: rt=arcsint, arccost, 0   As we know that; ddxarcsinx=11-x2ddxarccosx=-11-x2

Q: Question 6 Evaluate JJ xy dA, where R is the region in y = x2 R A) 13/7 B) 16/3 18 20 2.

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Q: Sketch the region enclosed by the curves and find its area. у %3 сos 9x, y —D 0, х - x = 18' 9 NOTE:…

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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: Find the volume of the solid generated by revolving the region R bounded by the graphs of the given…

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

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

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Q: Consider the function f(x): - 4x + 6x - 8. f(x) has a critical point at x A. Find the value of A: A…

A: For critical points ofa function we first find the derivative of the function and equate it to zero.

Q: Find div F and curl F if F(x, Y, z) = x°i – 4j + yzk. div F= curl F=

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Q: V4-x² c 3-x²-y² x dz dy dx J_5+x²+y² A 128/15 B 16/89 23/6 D) 6

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Q: Describe the graph of the equation. r = 7 cos t i – 17 sin t j +k O An ellipse in the plane z = 1,…

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Q: -4 = ニ 200

A: To solve for x using the the given equation.

Q: Find the area of the region bounded by the graphs of f (x) = x° and g (x) = Xx. A 1 в) 4 0.5 D 3

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Q: Find r(t) for the given conditions. r"(t) = -4 cos(t)j – 3 sin(t)k, r'(0) = 3k, r(0) = 4j %3D %3D…

A: Given

Q: 8. 1) Use the Integral Test to determine whether the series is convergent or dive n' +1 n=1 Please…

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Q: Sketch the region R of integration and switch the order of integration. P(x, y) dy dx F(x, y) dy dx…

A: Given: I=∫-22∫x24fx,ydydx The region bounded by the curves y=x2, y=4 from x=-2 to x=2 is shown…

Q: 1. A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of…

A: The solution is given in the next steps.

Q: Find curl (5z i + 6x j + 3y k). curl (5z i + 6x j + 3y k) = ( i )i + ( i i )k

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Q: Find the J(2x + 1)³ dx

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Q: find area OPShaded Pegion ニ 16x

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Q: Find V · (V × F) if F(x, y, z) = 10 sin xi + 5 cos(8x – 9y)j+ 4zk. V· (V × F)

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Q: Apply the Ratio Test to each series to determine whether the series converges, or state that the…

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Q: ||r'(t) x r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = t’i+t5j K(t) =

A: We have to find k(t)

Q: Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 А) 6 B) 9 12 15

A: Let's find.

Q: -Ive the derivative dy for the function: x dx = e'sint ; y = ecost %3D

A: To find dy/dx.

Q: dy If y = 3e5 . Find dz

A: Given query is to find the derivative of the expression.

Q: Let I be the flux of G = (2e", 4x°e*“, 0) through the upper hemisphere S of the unit sphere. (a)…

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Q: E(-1)n+1_2 Vn n=1

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

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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: xe*y dy dx

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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 area of the surface that is generated by revolving the portion of the curve y= x² between x…

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Q: Find V· (V × F), if F(x, y, z) = e*²i+3xe'j – 7e*k. V . (V × F) = x z evz 三

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Q: The strength E of an electric field at a point (x, y, z) due to an infinitely long charged wire…

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

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Q: What is the measure of the apothem of the hexagonal base? (c) What is the area of the hexagonal…

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Q: Find curl (8z i + 9xj+4y k). curl(8z i + 9x j + 4y k) = ( i )i + ( i j+( i )k

A: topic- curl of a vector