r2 cose dr de valuate the iterated integrals A) 1

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

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Q: Find curl (6z i + 7x j + 8y k). curl(6z i + 7x j + 8y k) = ( i )i + ( i )j + ( i )k

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = t'i+ t3j K(t) =

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

A: Since you have asked multiple questions in a single request we would be answering only the first…

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: Determine the area of the region enclosed by y3x^2 and y=x^1/2

A: To find the area of the region enclosed by the given curves.

Q: Solve [D* +3D² –4]y= 2sin° (5x)

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

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Q: a 0 0 0 0b0 0 0 0 c 0 0 0 0 d Using cofactor method, prove that det M = = abcd

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find curl (2z i + 3x j + 6y k). curl(2z 2z i + 3x j+ 6y k) = ( i )i + ( i j + ( i )k

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Q: y=x*(1-x)ª 4-4x 4+4x

A: Use the chain rule of differentiation.

Q: Find lim f(x) for the given piecewise function. x-4 2х + 5 if x 4 If the limit does not exist,…

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Q: Find div F and curl F if F(x, y, z) = 7e*i – 6 cos yj+ 6 sin? z k. div F= curl F=

A: DivF  and curl F are evaluated.

Q: Find the area of the region using a double integral. The region bounded by y = 4x°, 2x + y = 6, and…

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Q: Find the area of the region(s) enclosed by the curve y = |2x - 6|, the x-axis, and the lines x = 0…

A: Given: y=2x-6x=0 and x=4

Q: Find curl(3z i+ 4x j+ 8y k). curl(3z i+ 4x j + 8y k) = ( )i + ( i )j+ ( )k

A: We need to find curl of given vector.

Q: For neN simplty 2-글 + 4-1 +8-금+16-습+. + +2"-그 2n

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Q: Question 13 Evaluate JJ xy dA , where R is the region in fa, 3) (1, (5, 3) R (2, 1) (4, 1) x A 56 В)…

A: A detailed solution is given below.

Q: Calculate y" (x) and y" (x). бх — 6 y(x) (Use symbolic notation and fractions where needed.) y"(x) =…

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Q: 1. E(n + -3 2 n=1

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Q: Question 7 Find the area of the region(s) enclosed by the curve f(x) = x³, the x-axis, and the lines…

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Q: dx

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

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

A: Solution: ∯∂∂x6xy -∂∂y3xydxdy   (By green's theorem)

Q: 31.| CSC I COLI dt

A: We will use substitution method to solve both the integral.

Q: (a) Select the correct choice below and fill in the answer box within the choice. O A. lim f(x) =…

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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: d y Find dx? for the parametric equation: x = et;y3Dt³ +t+1

A: Find your answer below

Q: Find the approximate area under the curve of (X) = x²+1 from x = 0 to x = 2, using 4 left- endpoint…

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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(6,…

A: we have to find directional derivative.

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

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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: find in Verse, then domain t range 8-X\ = (x)} OD:[8,8),R:[O,00) 2 All Real Numbers 8.00

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Q: A. Sketch the figure for analysis. Shade the needed region and draw a representative vertical or…

A: Here, the region is bounded by the curves: x=4, y2=x

Q: Зху dx + 4xy dy %3D i 63

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Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

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Q: Find V. (V × F), if F(x, y, z) = 5e"*i+ 6xe®j– 2ek. V · (V × F)

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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: ,2 COS cos n Σ n3 n=1

A: Given problem:-

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: Evaluate the iterated integral. J. J, J vz dx dz dy A 45 в) 34 (© 47/3 D) 5

A: Topic = Integration

Q: Calculate the following derivative. (Use symbolic notation and fractions where needed.) d (15 Vsin…

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Q: sine "/2 Evaluate the iterated integrals r cos e dr de A 1/6 1/2 11/9

A: Explanation of the answer is as follows

Q: 86. If f'(x) > 0 for all real numbers x and s(1) đt = 0, which of the following could be a table of…

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Q: Find the limits of integration ly, uy, Ix, ux, Iz, uz (some of which will involve variables a, y, z)…

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

Q: The productivity of a major manufacturer of microwave ovens is given approximately by…

A: Given problem:- The productivity of a major manufacturer of microwave ovens is given approximately…

Q: Evaluate the integral by choosing a convenient order of integration: « сos(хy) сos1"(тӕ) dA; R —D |…

A: Given