Find the area of the region enclosed by the curves y = x² and y 4.x by integrating with respect to y. (4, 16) y = 4x NOTE: Enter the exact answer as an improper fraction if necessary. A y = x² 4 ||

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: 34 Count lim (1+x) F b) lim (1-x)* メ→0 The limit in (a) determines e. What special number does the…

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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: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) =…

A: The given function is: f(x)=e-5x

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Q: dy x+3y. dx 2x

A: First order differential equation :  Consider the first order differential equation…

Q: 25. dx is 1 (B) (©) ! (A) 2e (D) (E) divergent

A: see below the answer and calculation

Q: d Find [r(t) · u(t)] and [r(t) x u(t)] in two different way dt dt r(t) = cos ti + sin tj + tk, u(t)…

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Q: Find the volume of the solid generated by revolving about the y- axis the region bounded by the…

A: Given problem:- Find the volume of the solid generated by revolving about the y- axis the region…

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

A: Let's find.

Q: Find V × (V × F) if F(x, y, z) = 4xyj+2xyz k. V × (V × F) :

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Q: Find the S(x* +) dx xe-1 А. 1x? + c e-1 4e xe+1 В. Ix2 + c e+1 2e xe+1 С. 1x3 + c e-1 Зе xe+1 1 D.…

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

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

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Q: Solve [D* +3D² –4]y= 2sin° (5x)

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 4 cos(t)i…

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Q: Use a triple integral to find the volume of the solid. The solid bounded by the surface y = x and…

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Q: Evaluate the definite integral. 9ti +3t'j + Vtk) dt

A: The given integral,          ∫-119t i+3t3 j+t3kdt

Q: Use the first principles delta method to find the derivative of y = x2 – x. %3D

A: Here we have to find the derivative of y by using the first principles delta method.

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

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Q: (xy)=efr sin), Plo,0l Q(5,1)

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Q: 2. Compute Ja F · ds for F c(t) = (t , In(1+ t²), e*) for 0 <t < 1 VV, where V(r, y, z) = 4x² In(1+…

A: Find your answer below

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

A: Given

Q: H.W (5) Solve the following differential equations of (x'+y')dx+(2xy cos y)dy phee

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Q: Find the following for the given equation. r(t) = (e, 5t?, 6 tan(t)) (a) r'(t) = (b) r"(t) = (c)…

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Q: 10 Find div F and curl F if F(x, y, z) = xz°i+ 5y"x²j+ 4z?yk. div F= curl F=

A: Solution:

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

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

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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: ||r(t) × r"(t)|| Use the formula k(t) = to find k(t). 3 r(t) = e"i+ etj 9ts K(t) ||

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Q: 2 _9 ii)lim- t-3 t2+4

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

Q: 2. Prove that the p-series converges for p > 1.

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Q: Find the 4** x³ dx А. + c 4 In 4 В. + c 4 In 4 С. + c 3 In 3 D. 24 2 In 2

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Q: Evaluate the integral. (Use C for the constant of integration.) 2 cos (a) da sin(a)

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A: We have to choose the correct option from the given options according to the given information

Q: 17-20 Express the limit as a definite integral on the given interval. 17. lim sin x, Ax, t, [0, 7]

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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Q: 4 y=V4x- 2/2x

A: Topic = Derivative

Q: Graph the eauation - include local+ Absolut extreme Points if applicable - -include inflection…

A: maxima minima

Q: If 1 f(x) 1 .3 + 1 + x 4 X° + 3 then find f'(0) +

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Q: f(x, y) = x3 - y³, P(4, 3), v = (i+ j) %3D 2

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Q: 12. Find an equation for the tangent plane to the surface given by 2xy? = 2z2 – ryz at the point (2,…

A: We know that the equation of the tangent plane is: nxx-x0+nyy-y0+nzz-z0=0 Where n→-nxi+nyj+nzk is…

Q: 102: Find div F and curl F if F(x, y, z) = xz°i+ 5y1ºx²j+4z²yk. div F = curl F=

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Q: 2. Find the area of the parallelogram whose vertices are given by: P: (1,2, –1), P2 = (4, 2, -3), P3…

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Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 6x from (6,6) to (0,0). NOTE: Enter…

A: We need to evaluate the following line integral ∫C-ydx+xdy Where,  C: y2 = 6x  from 6, 6 to 0, 0

Q: Use the Babylonian's formula to calculate the circumference of a circle with diameter of 30 units.

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Q: +4

A: To check the convergence of the given improper integral:∫-∞2dxx2+4

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

A: To find dy/dx.

Q: (c) f''(x) = cos x, f(0) = 1, f'(0) = 2, f"(0) = 3.

A: Explained below