Find if the sequences diverges or converges. If converegs, find the limit. 1. an=n1/n

Q: Integrate completely

A: Solution-

Q: dr

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Q: (2×+5)2xー5 2x -5 3.

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Q: Find the directional derivative of f at P in the direction of a. f (x, y, z) = xy + z?; P(2,5, 2); a…

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Q: d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating d dt dt the product directly…

A: We know, d/dt (r1(t).r2(t))= r1(t).dr2(t)/dt + r2(t).dr1(t)/dt

Q: Linear equation of order one: dy-(x' -2xy kdx =0 Integrating factors fouund by inspection.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 3. Give the parametric and symmetric equations of the line that passes through the point (4,-3,5)…

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Q: (1-2=) dr

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A: Let's find.

Q: S(sec; - sin) do

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A: Use the derivative for the finding velocity of the function

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 3 1 lim t→+∞\ 7t2 +8'8t (?, ?)

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Q: Differentiate the following functions using logarithmic differentiation y = log√2x + 5

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Q: The origin of a coordinate grid is labeled A. Line segment AB forms an angle of 30° with the x-axis.…

A: find the components

Q: 2 dt 22. Evaluate o v9– 2t² 2 dy 3-y³ 24. Evaluate o v8-y'

A: 22)I=∫0129-2t2dtt=32 udt=32 duI=∫29-9u2 32duI=2 ∫11-u2 duI=2 sin-1uI=2 sin-12 t301I=2 sin-1(23)

Q: Suppose FW = Ax+B, with F6)-r and F() - 8, pind F) interms of A,B,r,s

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Q: By substituting y=xv, solve the given differential equation, (2xy+ x²) dy = 3y² + 2xy with dx the…

A: The given DE is: 2xy+x2dydx=3y2+2xy⇒x22yx+1dydx=3y2+2xy⇒2yx+1dydx=3yx2+2yx⇒dydx=3yx2+2yx2yx+1

Q: tan zdr

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Q: Consider a triangle ABC like the one below. Suppose that B=122°, a= 29, and c=59. (The figure is not…

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Q: Consider the vectors: å = ỉ– 3j + 2k , b' = 4j – 2k and ở = i + k in 3D A. Write 3a – 4 b - 2¢ in a…

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Q: Given the final result as I = 4        a) Trapezoid method and b) 1/3 Simpson method   Calculate it…

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Q: 2 = e" cos u = e – r, v= re".

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Q: N-1 22+2-1 if x0 type of discontinuity present.

A: Given query is to find value of x where f(x) is discontinuous.

Q: Find an equation of the plane that is parallel to the plane x + 2y – 7z + 15 = 0 and contains the…

A: A detailed solution is given below.

Q: 2.s +3 Find the Inverse Laplace Transform of (s+4) 3

A: Given

Q: A frameless painting with a size of 2 meters by 2 meters hangs on the side of a wall where its…

A: Solution of the problem as follows

Q: Evaluate the double integral where D is the region bounded бy у %3Dх, у%3D2х, х%3D1, х%3D2- 4ху dA

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Q: Find the Laplace transforms of the functions(use limit): a) f(t) = t^2 b) f(t) = t-2e^3t

A: Solve the following

Q: secotaned0 2sec0+3

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Q: . The linear differential equation dx 2 has the integrating factor equal to_ (Note: Simplify or…

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Q: S Le+6)dx (x+2)*

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Given

Q: x²– y² )² Consider the function f (x.y) =| x²+y², Which ONE of the following statements is TRUE? O…

A: We will find limit at (0,0).

Q: Let ū and v are vectors such that | ỉ| =4 and | ở | =5, and the angle between them (when joined tail…

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Q: The following vectors are in 3D. Write in a unit vector form and find its magnitude. а) k%3D…

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Q: A hydrologist needs to estimate the volume of the water in the approximately circular well as…

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Q: Find T(t) and N(t) at the given point. r(t) = 7 cos(t)i +7 sin(t)j; t = 3 T(-) .3 .3. ||

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Q: Given the differential equation y' = 4x y Find the next two Implicit derivatives of the differential…

A: The given differential equation is y'=4xy ............................................. (1)…

Q: Evaluate the definite integral by choosing the appropriate substitution. You must show your work.…

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Q: sify whether f(x) is continuous or discontinuous at the point/s. If disco x – 2 x <-1 f(x) = { x² +…

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Q: Differentiate the following without expanding 3x2-4 You may use the Insert -> Equation function to…

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Q: Find an equation of the plane through (1,8, 5) that is perpendicular to the line x – 2 = 3t, y + 3 =…

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Q: 11 of the distance from which it 12 A Super Happy Fun Ball is dropped from a height of 5 feet and…

A: This is a problem related to sequence and series. Based on the general formula and concepts we will…

Q: O »(x) = Given the differential equation y' = 8x + 4 y' and y (0) = 1 and its next few implicit…

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Q: 5g is moving horizontally with speed v o. Question 1: A bullet of mass m= hits a block of mass 100m…

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Q: Σ 2(3n 1) 6n + 4

A: The series is convergentsee below the calculation

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 5 cos(t)i + 11 sin(t)j +…

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Q: Find the arc length of the parametric curve. = 14 cos(t), y = 14 sin(t), z = 48t; 0<t <T

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Q: dæ Evaluate: x/9x² +4 A) None of the above V9x² + 4 + 2 B f (x) = -2 ln +C %3D 3x © s(12) = -- In f…

A: I=∫dxx9x2+49x2+4=t9x  dx9x2+4=dtdx=9x2+49x dtI=∫19x2 duI=∫1u2-4 duI=∫1(u-2)(u+2)…

Q: 1) Sketch the curve. a) r=-2 sin O r = -2 sin O Show All Work

A: Explanation of the answer is as follows