Convert the point with polar coordinates (4, to Cartesian coordinates. Enter exact values. The point is:

Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). v = (0, 6) %3D

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Q: Find f'"'(x), the third derivative of f, and f (x), the fourth derivative of f. f(x) = 7x* + 2x³ +…

A: In the original solution it had been shown that:  f4x=ddxf'''x=ddx168x+12=1681+0=168

Q: x- 9x + 3x? The limit of the function f(x) : as x approaches negative 3x-4+ 5x2 infinity is equal to…

A: Find your answer below

Q: Find the derivative of the function described. (Rx5) 3. f (x) = (1 +x + x² + x³ )'³

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Q: IM Given that > п+1 = 0.47199 determine the value of n3 n + 1 n=3 n3 n=5

A: This is a problem related to series and sum calculation. Based on the general formula and concept we…

Q: Give the curve r = 3 cos 0 a) Find the points on the given curve r = 3 cos 0 where the tangent line…

A: Explanation of the answer is as follows

Q: 1) Sketch the curve. a) r=-2 sin 0 Show All Work

A: Given

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

A: Given: R→=sin2t, cos2t,2t32, 0≤t≤1

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

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

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Q: (c) f(x, y) = V3x + y?, x = 2, y = 0, dx = 0.01, dy = 0.01. %3D %3D 1 f. 2/3x + y? 3 (i) 3x+y? (ii)…

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Q: (b) Find the distance from D to the plane containing A, B, and C. NOTE: Enter the ezact answer.…

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Q: Find the curve given by x = vt and y =(? – 4), t 2 0 find the slope and concavity at the point (2,…

A: Here, the parametric curve is given by: x=t, y=14t2-4, t≥0

Q: Homogeneous or Not? State the degree of the function. 4x^2-3xy+y^2

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Q: Consider the following differential equation. (x2 + y2)y′ = y2 Let  f(x, y) =  y2/x2 + y2 .  Find…

A: This is a problem of differentiation of the function. Based on the general formula we will answer…

Q: Determine if the sequence is increasing, and/or bounded. 3 — п (b) { (a) 1 — Зп - 3n n=1

A: Given

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: What can be concluded when integral test is applied to the following series? 1 (2n + 1)3 Select one:…

A: The given series is: ∑n=3∞1(2n+1)3 Let, an=1(2n+1)3, n≥3

Q: Sketch the region R whose area is given by the iterated integral. dx dy 3 3- 2- 2- 1- 3- 3 2 3…

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Q: The function f(x) is continuous everywhere. FALSE O TRUE 3.

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Q: x² sinh x dx

A: Let's find.

Q: dx x2 + 6x + 25

A: This question is based on definite integral.

Q: sint In(cos t)dt

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Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

A: Given functionf(x)=32x2/3differentiate w.r.t.xf'(x)=32*23x23-1f'(x)=x-13f'(x)2=x-132f'(x)2=x-23we…

Q: Use a double integral in polar coordinates to find the volume V of the solid bounded by the graphs…

A: Given problem:- Use a double integral in polar coordinates to find the volume V of the solid bounded…

Q: Determine if (6x + y^2) dx + y(2x - 3) dy = 0 is exact or not

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Q: Set up and evaluate the integral for finding the area and moments about the x- and y-axes for the…

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: We have to find the volume of the given region according to the given information

Q: Find the area of the region enclosed by the rose r= 20 cos 30. NOTE: Enter the exact answer. A %3D

A: Solution is given below:

Q: Verify that the two planes are parallel. -x + 6y + 2z = 7 %3! +3y +z 8 Find the normal vector, n,,…

A: We have to check whether the given plans are parallel or not or we have to find distance between the…

Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). %3D %3D v (0, 6) %3D b =

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Q: 1. For each of the following, state whether the equation is ordinary or partial, linear or…

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Q: Verify Green's Theorem by evaluating both integrals ƏM y2 dx + x2 dy = dA ду for the given path. C:…

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Q: It is determined that the value of a piece of machinery declines exponentially. A machine that was…

A: A machine that was purchased 5 years ago for $66000 is worth $36000 today.

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

A: Given problem:-

Q: Find a and b such that v-au bw, nhere u-(1, 2) and w- (1. -1) v - (4, 5)

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Q: Find the arc length of the parametric curve. x = 3 cos(t), y = 3 sin(t), z = 4t; 0<t<+ L =

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: Use the Quotient Rule to find the derivative of the function. See Examples 4 and 6. 6t? - 5 f(t) :…

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Q: 3. y = Vx*

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Q: Find the component form and magnitude of the vector v with the given initial and terminal points.…

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Q: A region bounded byf (y) = Vỹ + 1, y = 4, y = 9, and x = 1 is shown. What is the volume of the solid…

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Q: п+1 Given that 0.47199 determine the value of ) n +1 n3 n=3 n3 n=5

A: Given: ∑n=3∞ n+1n3 =0.47199 To evaluate: ∑n=5∞ n+1n3

Q: 2. tanh-'x + lny1 – x²

A: We have to find derivative

Q: Using the Maclaurin series for arctan(x), find the Maclaurin series for the given function. f(x)= -7…

A: Maclaurin series of arc tan (x)= ∑k=0∞ (-1)k x2k+1(2k+1).

Q: 0/ifit was FCかy)2165(6w)30 2 -36 y? cos (6XY) .3 =36 Y'cos (6X4) -36 y'cos (6xY) 2. = 36 y'cos (6XY)

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Q: a. Determine "(®) if fx) = (8x² + x)³. Write your answer in simplified form. %3D b. Determine

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Q: 4x? ds where Cis the portion of the curve y y° 1 =- from Evaluate the line integral (1,1) to (2,4).

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: Solve the initial value problem. 2x(y + 1)dx – ydy = 0, where x = 0 and y = -2. %3D %3D

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Q: 2(у - 4x?)dx + хdу %3D 0. x²y = 2r* + c

A: