Find the general antiderivative F(x) + C for the function. f(x) = 12x + 67 O 6x² + 6x + C O 6x2 + 6n°x + C O 6x2 + n°x + C O 6x2 + n5 + C

Q: Determine whether the following series converges or diverges. Σ 5n2 +5 n=1

A: We can solve the given problem as follows:

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A: Here, the given integral is: ∫091xdx

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Q: (x + y)ds, C : ¤ = 2t, y = – 2t + 3, for – 3 <t<0. Preview

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Q: the surface generated by revolving about the y-axis the part of the Find the area of 2 curve y = x…

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Q: The term a,6 of the sequence {an} given by (2 3 4 5'7'9' 11

A: Follow the procedure given below.

Q: (d) (u v)v (e) u (3v)

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Q: Business Decisions Sharon, the owner of the Brentwood Motel, is planning to renovate all the rooms…

A: Answer is in below steps.

Q: Find the arc length L of the graph of r(t). r(t) = 6 cos(t)i + 6 sin(t)j + tk, 0<t< 2n 0 <t< 2n L =

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Q: Find the direction cosines and angles of u and show that cos a + cos B + cos? y = 1. (Round your…

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Q: C. VARIATION OF PARAMETERS 1. (D² + 1)y = secx tanx 2. (D2 – 3D + 2)y = 1 1+e-x

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Q: 3. The value of a certain baseballcard (in dollars) tyears after 2015 varies according to the…

A: Given function describes value of card t years after 2015

Q: 3. y = Vx*

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Q: Evaluate the double integral over the rectangular region R. 9xy*dA; R = {(x, y): – 1 < x < 1, - 5 <…

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Q: Calculate the iterated integral. 36 9. )dy dx + 1

A: Given problem:-

Q: Consider the following. u=i+j+k v = 2i +ì-k Find u x v. Determine if uxv is orthogonal to both u and…

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Q: 5. Find the derivative if yyx – 8 = xy + 2

A: yx-8=xy+2Differentiate w.r.t x

Q: C. VARIATION OF PARAMETERS 2. (D² – 3D + 2)y 1+e-x

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Q: Use limits to determine all the linear asymptotes of 3x2 – 5 if a1. a² + 2x – 3'

A: Let's find.

Q: Bones from the skeleton of a fish have lost 30 percent of their carbon-14. Note that for carbon-14,…

A: Formula  Given  k = 0.000124 It lost 30 percent of carbon  The left is 70 percent

Q: Use the quadratic formula to solve forx. 5x+5x-1 0 (If there is more than one solution, separate…

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Q: Solve the following differential equation using variation of parameter. 1 y" + 3y' + 2y 1+ et

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Q: The base of a three-dimensional figure is bound by the circle x² + y? = 9. Vertical cross sections…

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Q: Find T(t) and N(t) at the given point. r(t) = = 8 cos(t)i + 8 sin(t)j; t 3 T 3 N(5) = 3

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Q: 1. A light hangs 15ft above a horizontal path and a man 6ft tall is walking away at 5 ft/sec. i) How…

A: According to bartleby guidelines when student post more than one question then expert must have to…

Q: Given the series: k=0 does this series converge or diverge? O diverges converges If the series…

A: The given series is ∑k=0∞-16k. To check convergence of the series we use ratio test. Suppose we have…

Q: Evaluate the indefinite integral. | x34 sin(x35) dx

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Q: Find an equation of the plane that passes through the points (-2, 1, 1), (0, 4, 7), and (1,0, –1).…

A: The plane that passes through the point,       -2,1,1, 0,4,7 and 1,0,-1

Q: Determine the interval(s) on which the vector-valued function is continuous. (Enter your answer…

A: The objective of the question is determine the interval in which given vector-value function is…

Q: List the first 5 terms of the sequence. 32 + 3n3 22 1 (а) ап — 3n3 n2 + 3n3 4 (b) (-2)n+1 + 3n 3n3…

A: a)an=13n3+223n3+323n3+......+n23n3b)4-2n+1+3nn=1∞

Q: Find the gradient of the function at the given point. 2 = In(x2 – y) - 9, (2,3) Vz(2, 3) = Need…

A: This is a problem related to derivation. Please follow the procedure given below for solution.

Q: Find the arclength of the curve x = 3t + 5, y = 4t + 7 with 2 < t < 5.

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Q: Sketch the region of integration. (Select the correct graph.) "In 3 dy dx In y y y

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Q: 1. y' + 2y = x²y³ .2.3

A: Given problem:- solve the given differential equation y' +2y=x2 y3

Q: The graph of x? + y² + 2y – 8x + 17 = 0 is a circle. O FALSE O TRUE

A: The given problem is solved below in detail.

Q: Given the series: 1 1+ - 6. 1 1 + ... 36 216 does this series converge or diverge? O diverges…

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Q: The position of a particle moving in a straight line is given by s) = - 8² + 28t, where s(t)…

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Q: The function given below is discontinuous at x = 1 - 4 I1 O TRUE O FALSE

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Q: Find the mass and center of mass of the lamina bounded by the graphs of the given equations with a…

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Q: F the curve. -)i + sin(nt)j

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Q: Test the series for convergence or diverg-

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Q: Find the mass of the sphere x2 + y2 + z2 = a2 where the density at any point is two times the…

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Q: Find the length of arc of the given curve.

A: Given: R→=sin2t, cos2t,2t32, 0≤t≤1

Q: Consider the following. 3D(6,-1,0) v = (-2, 3, 0) u = %3D Find u x v. Determine if uxvis orthogonal…

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Q: Consider the function f(x) 1 on the interval 4, 8]. Find the average or mean slope of the function…

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Q: Find the volume of the solid bounded by the graphs of the given equations.   z = xy,    z = 0,…

A: Given problem:- Find the volume of the solid bounded by the graphs of the given equations.   z = xy,…

Q: d?y +5xy = 0 dx +(sin x) 2 dy +2 dx dr3 = 1 dx2 O Option 1 O Option 2 d²y +3y dy dy dx? +y = 5x dy…

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Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); fi-) U =

A: we can solve this as follows: