0 and the length of the indicated Find the arc length parameter from the point t portion of the curve: (a) r(t) = (4 cos t, 4 sin t, 3t), 0 < t< 2

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Q: Find the radius and interval of convergence, R, of the series. E-1 n!

A: Answer is in below step.

Q: Find a number whose difference from its square root is least

A: Explanation of the answer is as follows

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Q: Find f'(x) and find the equation of the line tangent to the graph of f at x= 2. X-6 f(x) = 5x - 1

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Q: Consider the region bounded by x = 3y and x = y^3. A solid is formed by rotating the region about…

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Q: 3. Let f(r, y) = I sin ry. Find: %3D (a) fa(1,9) (b) fy(r, y) (c) fyy(I, y) (d) fyz(I, y)

A: Given,            fx,y=xsinxy

Q: 6. Let u = (1, 0, 2) and v = (2, -2, 1). 6.1. Determine 2 u-3 v in component form. 6.2. Find a unit…

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Q: n(x) = csc²(;2) Select the correct response: 1 1 CSC + cot(5) - 1 sec"(5e) tan(-e) csc²(-x) cot(r) 2…

A: We have to find the derivative of the above equation.

Q: Question 7 of 10 f (x) = x – 6x² + 9x - 2 Select the correct response 2.x2 + 12x – 9 - 6x - 12 372 –…

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Q: Assume a population of fish grows exponentially. A pond is stocked initially with 500 fish. After 6…

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Q: QUESTION Determine the length of the missing side of the right triangle below. Round your answer to…

A: The given triangle is:

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Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is…

A: This question is related to infinite series, we will solve it using given information.

Q: 2. (6x -2) dj d2

A: We have to find the double integral.

Q: Using "Numerical Differentiation (Backward Finite Difference)" Problem Solving f(x) = 2cos (3x-2)…

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Q: Find the volume of the pyramid with base in the plane z = and sides formed by the three planes y -9…

A: To solve the following problem

Q: Describe the graph of the equation. r = 19 sin 10t i – 19 cos 10t j O Itis a parabola in the…

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Q: A tank is discharging water through an orifice at a depth x (m) below the surface of water whose…

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Q: (5+9)4x - (xx) dg = o

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Q: HimilFind the akeas fak the folfewing regions Area of theregion insidethe circle (r=1)and outside…

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Q: 3. Find two different sets of polar coordinates (r. 8) for the point with Cartesian coordinates (x,…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

A: Directional derivative

Q: 2. For each of the following functions, determine the derivative using only algebraic techniques and…

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Q: Show tkat cos (2 I +x

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

A: Given,            fx,y,z=xy+yz+xz , P8,9,-8 , v=16i+j-kTo find : Find the directional derivative of…

Q: The auxiliary equation for the differential equation y" – 4y" – 12y = 0 - is

A: The given problem can be solved as follows:

Q: Find an equation of the plane. The plane through the point (7, 8, 1) and with normal vector 3i +j -…

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Q: x2 - 5x + 6 A and X-6 Bx+C (a) The given integrand can be split into factors- x+1 (b) The given…

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy = -54 -36

A: In this question we have to find integration by using triple integration.

Q: For time, t, in hours, Osts1, a bug is crawling at a velocity, v, in meters/hour given by 7 v = 6 +t…

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Q: 3. Find a power series representation for the function. (Give your power series representation…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 5. Use the Laws of Logarithms to expand the expression. x + 2 3 (a) log (b) In y (c) log. x(x² + 4)

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Q: Find an equation of the plane. The plane through the points (2, –1, 3), (5, 3, 6), and (-3, -3, -3)

A: We are asked to find the equation of the plane

Q: Evaluate the integral 24 11) dx, by making the appropriate substitution: u = Ja* (2* – 11)*“dz =

A: ∫ un du =un+1n+1+C

Q: Describe the graph of the equation. r = 8 cos t i – 17 sin t j + k O An ellipse in the plane x = 1,…

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Q: Two linearly independent solutions of the differential equation y" + 2y' + 4y = 0 are Select one: O…

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Q: 11. Find the slope of the tangent line t = 2. Show all your worka x = v2t, y =t %3D t

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Q: Provide a step-by-step solution to the following differential equation (linear quation) y' =…

A: The given differential equation is; y' = x-2ycot(2x).

Q: Find an equation for a parabola with focus (7,-2) and directrixx = = 4.

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Q: Find the limit. lim (t i – 3 j + r² k)

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Q: Find an equation of the plane. The plane through the point (2, -8, -1) and parallel to the plane 7x…

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Q: (b) Find the points in which the required line in part (a) intersects the coordinate planes. point…

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Q: Admission to a baseball game is $3.00 for general admission amd $4.50 for reserved seats. The…

A: Let, x be the number of general admission tickets.  y(=1357-x) be the number of reserved tickets.

Q: Question 6 of 10 n(x) = csc°(;w) Select the correct response: csc(-a) + cot(x) CSC - 1 sece'(승)…

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Q: A small hula-hoop was rolled on the ground.  After rolling exactly 6 times, it went 37.7 feet.…

A:

Q: #2. Determine if the function g(x)-3x+5x is even, odd, or neither (a) using algebraic approach, (b)…

A: Odd even function

Q: Solve the system of equations. x+2y = 0 8y = - 4x Solve the first equation for x. x +2y = 0 x = y

A: x+2y = 0 8y = -4x 2y = -x put this in equation  so the the equation has infinite solution    x + 2y…

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x³ – y³, P(6,…

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Q: The Maclaurin series for cos x is Eo (-1)"; What is the n%3D= (2n)! coefficient of the term forx*?…

A: