Set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the x-axis. y 16 - x2 16- 14 12 10 y 8- 6 4- 2- 2

Q: Find the volume of the solid that is bounded by the surfaces z = 152 - x2 - y?, z = 0, x = 0, y = 0…

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Q: Calculate the arc length of y = 3x + 3 over the interval [0, 3]. (Use symbolic notation and…

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Q: Suppose a population function P(t) satisfies the following differential equation. P is measured in…

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Q: Find the general solution of the following differential equation. y''' +y'' + 3y' −5y = 0 [Hint:…

A: Use the auxiliary equation for finding the other roots and general solution.

Q: S- x+dx Using trigonometric substitution, (1+x?) tan4ode A sece В None tan+Od0 sec20 sin4ode (D coso…

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Q: Assignment On Integral of Trigonometric Functic Determine the integral of the ff. functions. 1. S -…

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Q: Find dy for dx 1. e*y = e4x – e5y ху

A: exy=e4x-e5yDifferentiate with respect to yyexy+xexydydx=-5e5ydydx(xexy+5e5y)dydx=-yexy

Q: Find div F and curl F if F(x, y, z) = x'i – 3j + yzk. div F= curl F=

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Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve).…

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Q: Adjust the domain of the rectangular equation, if necessary. y = x^2-7

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Q: A rectangular tank with a square base, an open top, and a volume of 5324 ft is to be constructed of…

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Q: An iceberg travels due South at 15 km/h in a fast Labrador Current. A passenger ship, 50 km to the…

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Q: S- x³dx is equivalent Vx²-4 Using trigonometric substitution,

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Q: Find the value of n in the following definite integral. S“ 4x*dx = 1

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Q: One of the correct steps to evaluate x2Inx dx to yield the correct integral x³Inx A x² dx 3 O ---fa…

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Q: Consider the following. RX) = x In x², (-1, 0) (a) Find an equation of the tangent line to the graph…

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Q: Find the area of the region bounded by y = (1/8)(-x² + 6x +7) and y = -6. Answer:

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Q: Evaluate: /x*V1-x*dx A None 3 글(1-x4) 2 +C В 3 -(1-*) C 3 (D (1-x+) +c - C 3 은(1-x) 2+C

A: We have to solve above question and find integral

Q: Find the partial derivative. f(p, q) = e=

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Q: ||r(t) x r"(t)|| ||r'(t)||* Use the formula K(t) to find K(t). r(t) = 4 cos(7t)i+ 4 sin(7t)j + 3tk…

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Q: Given =16,-2,k) and V=14,-4, 0]. Determine the value(s) of k if the angle between ü and v is 60°.

A: We will find the possible values of K as shown below

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

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Q: cIn2 e*dr = } 1 So Select one: O True O False

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Q: The position of an object attached to a spring is given by (t) 3 cos(4t) – ¿sin(4t). where t is time…

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Q: du for the integral dx du un dx Identify u and dx. | (5 – 6x?)5(-12x) dx u = du dx

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. ti +t dt

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Q: 4. Use partial fraction decomposition to evaluate dx x' + 4x +3 2

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

A: Green's theorem states that for  counterclockwise direction∮CPdx+Qdy=∬R∂P∂y-∂Q∂xdxdy

Q: ired) and other rules; You can use technology

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Q: integral using ir

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Q: a) fr'(2+x*)'dx bf sin(nx) dx )fx* In xdx

A: According to guidelines  we must answer only three of multipart questions. Please resubmit the…

Q: Write an equation for the ellipse that has vertices (+7,0) and co-vertices (0, +6). Provide your…

A: Vertices : (7,0) and (-7,0)Co-Vertices: (0,6) and (0,-6)Vertices are of the form : (h±a , k)h+a=7 ,…

Q: Find the PV of an income stream that pays out continuously at a rate of R(t) = 3000e0.1" dollars per…

A: Given problem:- Find the PV of an income stream that pays out continuously at a rate of R(t) =…

Q: Evaluate the line integral |-ydx + xdy along the curve C : y² = 24x from (24, 24) to (0, 0).

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Q: A cylindrical can is being filled at the rate of at =3t" , h(t) describes the height of the…

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Q: Find V. (V × F) if F(x, y, z) = 7 sin xi + 2 cos(2x – 3y)j+ 6zk. V·(V × F)

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Q: y" + y = sec 0 tan 0

A: The given differential equation is  y''+y=sec(theta)tan(theta).

Q: Let 7 (t) = (3t2 – 1,t? – 2t3, Find the line (L) tangent to r(t) at the point (11, – 12, – 64) –…

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Q: Describe the graph of the equation. r = 3 cos t i – 18 sin tj+ k O An ellipse in the plane z = 1,…

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Q: The absolute value of the complex number [2 + sqrt (2) + pi] +j [e- sqrt (3) + 5] O 8.88 O 11.5 O…

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Q: Use cylindrical coordinates to calculate SS lw f(x, y, z) dV for the given function and region: f(x,…

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Q: Find the tangential and normal components of the acceleration vector for the curve 7(t) = (- 3t,…

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 5y*x²j +4z²yk. div F= curl F=

A: To find curl F and div F.

Q: 2n Graph the sets of points whose polar coordinates satisfy the inequalities Osrs1. Choose the…

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Q: dx 2. x²V4-x?

A: Just use the trigonometrical substitution to make integral easy and then solved it.

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

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Q: S- dx x?V4-x?

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Q: Ty csc?y dy is equal to A —у сoty — coty dy - Scon dy у сoty coty dy с) -у соfу+ coty dy D) None E у…

A: Integrate by parts.

Q: T/3 sin4xdx = 4 T/12 Select one: O True O False

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Q: Find the speed of the curve F(t) = (4cos (t), 4 sin(t), 6t) at t = 3 %3| Speed =

A: Consider the curve  r(t)=<4cost2,4sint2,6t>