Find a formula for the nth term of the following sequences: а (a) ... an (b),,,... bn Assume a starting index of n = 1.

Q: 2. Calculate the Jacobian of the coordinate change (x, y, z) to cylindrical coordinates (r, 0, z).

A: To calculate the Jacobian of the coordinate change  to cylindrical coordinates .

Q: Find all relative extrema of the function f(x) = x^4 − 4x^2 + 2 by using the Second Derivative test…

A: Find the relative extrema of the function.

Q: Consider the function below. h(x) = (x + 2)77x - 3 (a) Find the interval of increase. (Enter your…

A: h(x) =( x+2)7 - 7x-3h'(x) = 7(x+2)6 - 7     [as derivative of xn = nxn - 1]h''(x) = 42(x+2)5…

Q: For a certain stretch of road, the distance d (in ft) required to stop a car that is traveling at…

A: we find solution set in the interval notation.

Q: Determine whether C(A + B) is defined. If it is defined, express the result as a single matrix; if…

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Q: ind an equation of the plane with the given characteristics. The plane passes through (0, 0, 0), (5,…

A: Given that the point (0,0,0) ,(5,0,7) and (-4,-1,4) we have to find the equation of the plane…

Q: Find dx/dt,dy/dt, and dy/dx for  x=4te^t, y=8t+sin(t)

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Q: 5. The pair of equations dx dt dy dt = -5x + 2xy = −4y + 3xy = models two coexisting species with…

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Q: Let A(z) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t =…

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Q: Determine the limit of the sequence or show that the sequence diverges by using the appropriate…

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Q: Use the graph shown to find the following. (a) The domain and range of the function (b) The…

A: As we can see from the graph, the vertical asymptote is: x=1So the domain is

Q: Practice 3: Let 2(x) = F(x)/G(x), where F and G are the functions whose graphs are shown below. Find…

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Q: (b) Use Elimination by. Addition method 2x + y = 1 3x - 2y = 5

A: 2x+y=1⟶(1)3x−2y=5⟶(2)

Q: Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. lim (15 tan…

A: y=limθ→π2−(15tan⁡θ)15cos⁡θ

Q: Find in terms of ¤ and y for the curve y² = x³. d'y dx²

A: We have to do implicit differentiation

Q: Two poles are connected by a wire that is also connected to the ground. The first pole is 50 ft tall…

A: Given:To Find:

Q: Find the derivative a. f(x)= 6/(3x2-pi)4 b. f(x)=((3x2-pi x)4

A: (a) given,

Q: Evaluate the limit using L'Hospital's rule if necessary 3 (+)* 1+ lim +-+00

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Q: The mass of a length of wire is m(r) = x(1+2√7) kilograms, where r is the length of the wire…

A: The mass of a length of wire is  given by

Q: Evaluate the following integral /6 sec¹ zdz

A: The given integral is 6sec4x.

Q: Question34 If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 50…

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Q: s, is in metres, and t2 0. Find the acceleration of the car at the instant when the car reverses…

A: To find the acceleration when the car reverses direction, we first need to determine when the…

Q: Find the area of the surface generated by revolving the curve about the x-axis. 1==32²₁ 15 y -x³,…

A: .

Q: -x²/4-y²14 Consider the function F(x,y) = e and the point P(3, -3). a. Find the unit vectors that…

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Q: ∞ Write out the first few terms of the series Σ n=0 3 on (-1)^ 57 What is the series' sum?

A: Formula for sum of infinite G.P. = a/(1-r) Where, a = first term r = common ratio

Q: Complete the table. y = f(g(x)) y = (6x - 1)4 u = Need Help? Read It u = g(x) y = f(u) =

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Q: Derivative Rules: 1. Power Rule: (2”) = n d dx Special Case of this: (√T) 4. Quotient Rule: (²) ₁- V…

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Q: 8 Find the sum of the series Σ η = 1 20 (5η – 3)(5n + 2)

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Q: You are constructing a cardboard box from a piece of cardboard with the dimensions 2 m by 4 m. You…

A: We are given a cardboard with dimensions .

Q: 4. Solve, x+3 11 = 3 x + 8

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Q: The graph shows the influence of the temperature T on the maximum sustainable swimming speed S of…

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Q: 1. Power Rule: d dx Special Case of this: (x²) = nx" 4. Quotient Rule: n-1 U ( ² )' = d dx 2.…

A: C(x)= (5 x-2 )( 3 x2+ 4 x)We have to find marginal cost and for this we have to differentiate C(x)…

Q: Find the horizontal and vertical asymptotes. (Let n represent an arbitrary integer. Enter your…

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Q: Given √√² + 4y = x, find Answer Attempt 3 out of 4 dx in terms of x and y.

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Q: Find the critical points of the following function. Use the Second Derivative Test to determine (if…

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Q: Consider a pizzeria that sell pizzas for a revenue of R(x) = ax and costs C(x) = b + cx + dx2, where…

A: Consider the revenue and cost functions

Q: 4. Students were asked to formulate the system of equations needed to solve the following problem:…

A: Let x = amount of beansLet y= amount of bread

Q: Let f(x) = x³ + 6x² − 15x + 10. (a) Find f'(x) = (b) Find f"(x) = (c) On what interval is f…

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Q: Suppose that 3 J of work is needed to stretch a spring from its natural length of 34 cm to a length…

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Q: The projected year-end assets in a collection of trust funds, in trillions of dollars, where t…

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Q: Find equation of the tangent to the curve at the given point x=t^2-4t, y=t^2+4t+1; (0,33)

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Q: 2. Some psychologists have said that the hours is given by f(t)= (a) How many facts are remembered…

A: Consider the function

Q: The circumference C of a circle is a function of its radius given by C (r) = 2πr. a. Express the…

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Q: Find a formula for the nth term of the sequence below. -6, 6, -6, 6, -6, ... Choose the correct…

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Q: A ball of radius 15 has a round hole of radius 8 drilled through its center. Find the volume of the…

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Q: Use implicit differentiation to find the points where the parabola defined by x2-2xy+y2+4x-8y+24 has…

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Q: Find the cartesian coordinates of the point  (4,3π/2) (√2, π/4) (-9,-π/6)

A: To find the Cartesian coordinates of the following points.

Q: Find the exact length of the curve. x = 9 cos(t) - cos(9t), y = 9 sin(t)- sin(9t), 0 stST

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Q: S 1 In(7x) dx

A: I=∫1eln⁡(7x)dx

Q: Which of the following are solutions to: 2 ln x² - ln x + 2 + C x² x+2 In + C x4 (x + 2)² O2ln |x|-…

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