What is the closed form for the infinite geometric sequence beginning  4,2,1,1/2 where the first term is obtained by setting the index variable n equal to 1? The closed form is xn =

Q: 2) [3 Solve the IVP: y" - 6y + 8y = 0, y(0) = 0, y' (0) = 2.

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Q: The value of the integral is equal to: Select one: O 4 O с صرا من م من ته 3 x ²² (4x - 4y) dy dx

A: The given integral is: I=∫01∫0x4x-4ydydx   As we know the Power rule: ∫xndx=xn+1n+1+C

Q: 2 -2 [ 3x² + 4y dy dx = [[ 3x² + 4y' dx dy. We have Select one: True False

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Q: The Integral ffyr² dydx can be written as Select one: O So yx² dady Spa

A: Need to change the order of the integration and select the correct option. Given information: The…

Q: Find f'(x) if f(x) = -7x5 +4√x. f'(x) =

A: To find derivative f'(x)

Q: Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t > 0. Then…

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Q: : Find the orthogonal trajectories of the family of curves y4 = kx³. (A) ³ + 3x² = C (B) 2y³ + 2x² =…

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Q: Question 1 enclosed by Given the region D in R² y = 0, y = 1, x = 0, x = y² a. b. [ integral Sketch…

A: Given :- y=0,y=1,x=0 and x=y2 To find:- Sketch the region D Compute ∫01∫0y23y3exydxdy

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Q: .1.2

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Q: A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The…

A: Given problem:- A farmer is building a fence to enclose a rectangular area consisting of two…

Q: In evaluating 4 S²- 2dx -, is same as evaluating lim cos-¹(f(x))|4. Determine the value of of f(x)…

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Q: The double integral ydxdy equals: Select one: OA. 84 OB. 52 OC. 44 O D. 56 O E. None of them

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Q: Given: f(x) = x³ – 6x² − 15x + 7. Find the LOCAL MINIMUM point of f (x). A. (5, ƒ (5)) B. (−1, ƒ…

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Q: The gradient vector of g(x, y) = at (√√2,-1) is Vg(√2, -1) is equal to Select one: O True O False -

A: Given: The gradient vector of g(x,y)=x22-y22 at (2,1) is ∇g(2,1) is equal to <2,1>

Q: 2. A differential equation that is a function of x only O will produce a slope field with parallel…

A: Here, given that the differential equation is a function of x only. So, dydx=f(x)⇒y=F(x)+C, where…

Q: (c) Use the ratio test to determine whether the series is absolutely convergent, conditionally…

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Q: A boat is being pulled toward a dock as shown in the figure to the right. If the rope is being…

A: Let X be the distance of boat from dock (which changes with time ) And y be the length of rope  (…

Q: Evaluate the integral by applying the following theorems and the power rule appropriately. Suppose…

A: This is a basic integration formula

Q: The function f(x, y) = -2x² + 4y? - 11 has a local minimum at the point (0, 0). Select one: O True O…

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Q: en differential equation by undetermined coef y = x²ex + + 3

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Q: Give an example of a function f (x) that has one  positive derivatives on the range (−1, 0) and a…

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Q: Consider the function f(x, y) = y ln x - x ln y - . a Find the directional derivative of f at the…

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Q: Classify the following diferential equations. Write the order, linearity and the homogeneity of the…

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Q: Evaluate plti 5. S z² dz using the formula [2² dz = A 3

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

Q: The values of two functions, f and g, are given in a table. One, both, or neither of them may be…

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Q: c) Consider the series: 5-1+ 5 25 + .. i) Is the given series a geometric series? Explain. ii)…

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Q: A particle is moving with the given data. Find the position of the particle. 12. a(t) = 3 cost - 2…

A: 12) a(t)=3cost-2sint, v(0)=4, s(0)=0 13) a(t)=a, v(0)=v0, s(0)=s0.

Q: Evaluate the iterated integral: I 7-x X -SS e dyda 8 7 2

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Q: Find the volume bounded by 3x+2y+z=12 bounded by x=0, y=0, z=0

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Q: 5. Find the length of one arch of the cycloid x = sin and y = 1- cos 0

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Q: Use spherical coordinates to find the volume of the region bounded by the sphere p = 30 cos p and…

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Q: = Find the area A of the region that is bounded between the curve f(x) = ln (x) + 1 and the line…

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Q: Determine where, if anywhere, the function f(x)=x3+9x2−48x+2f(x)=x3+9x2−48x+2 is not changing

A: This is a application of derivative problem

Q: Consider the following problem. Find the distance traveled In 15 seconds by an object traveling at a…

A: Given:          Velocity vt=20+6cost          time t=15 seconds We need to find the distance…

Q: Simplify 8logg(64)

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Q: Q2) [ Given the function f(x,y)=x²-6x+y²-6y+8 a) [ Find all critical points of f. b) Find the…

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Q: Which of the following is the critical point of the function f(x, y) = x²y — xy? - Select one: O…

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Q: Ise spherical coordinates to find the volume of the region bounded by the sphere p= 20 cos p and the…

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Q: ·(2+ (2+x+31) dr by interpreting it in terms of areas. 9. Evaluate

A: Need to evaluate the integral by interpreting it in terms of areas. Given information; The integral…

Q: State the equation of f(x) if D = {x = R | x = }} and the y-intercept is (0,2). x + 1 a) f(x) = 3x+2…

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Find the absolute maximum and absolute minimum values of the function, if they exist, over the…

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Q: An oil tanker aground on a reef is forming a circular oil slick about 0.2 foot thick. To estimate…

A: Given,  Figure :

Q: Which of the below double integrals has the following region? -1 5 4 3- 2 -1 0 Select one: None of…

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Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent.…

A: topic- sequence and series

Q: 2. Find the local maximum and minimum values and saddle points (if any) of the function f(x, y) = xy…

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Q: Given the graph of f'(x) below, where the Domf (x) = (-∞, ∞). Find the interval(s) for which f (x)…

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Q: Evaluate 112x (2x - y) dx + (x + 3y) dy. C: x-axis from x = 0 to x = 6

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Q: Evaluate the following iterated integral without technology. π/15 π/15 cos 0 s s II Sp² sin cos…

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Q: Find the associated exponential decay or growth model. (Round all coefficients to three significant…

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