Find the inverse Laplace transforms of the functions: 3 (a) F(s) s4 1 (b) F(s) (c) F(s) = s+5 3s+1 s2 +4

Q: a) Find the fifth term of the sequence 16 31 46 61 9. 15 21' 27 b) Find the general term of the…

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A: The given integral is  ∫ee8lnx3x dx we solve the integral using proper substitution in the integral.

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Q: 5. y" – 3y' +2y=0; y1 =e*, y2 = e2x; y(0) =1, y'(0) =0 %3D -

A: Here is the solution:

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Q: 10 11 Suppose f(x) dæ = 6 and | f(x) dæ = 5. 10 11 Then f(x) dæ -

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Q: Evaluate. (Be sure to check by differentiating!) dx, x -2 4 + 2x dx 4 + 2x (Type an exact answer.…

A: To evaluate: ∫14+2xdx Let I= ∫14+2xdx

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Q: First four terms of the sequence n2+3 n 1+8 n are: 4 10 79 28 9 17 75 33 none 4 10 18 28 9. 17 25 33…

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A: Polar form

Q: Use the given graph to estimate the value of each derivative.  (a) f ′(−3) (b) f ′(−2) (c) f ′(−1)…

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Q: b) Find the exact area of the region enclosed by the curve y = x² – 3x, the x-axis and the vertical…

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Q: Suppose F is an antiderivative of f(x) = VT. If F(0) 1 then F(1) 4 %3D %3D is 3 A. –1, B. -, C. 0,…

A: Let f be a function . Suppose F is a function such that  F'(x) =f(x) then F is an antiderivative of…

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Q: Solve the equation: (x² – xy + y² )dx – xydy = 0. %3D O (v - x) el:) = (v - x) e(G) = c O (v - x) =…

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Q: Use the formula k(t) ||F(t) × r"(t)|| to find k(t). ||r(t)||° r(t) = 11 cos(t)i+11 sin(t)j+6tk K(t)…

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Q: Let f: R →R be defined as Sr + 2, if a < 1, 1-2a, if a 21. S(1) Plot f(r) of f of all r) Based on…

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Q: A region bounded by f(x) = 5 -x, y 1, and x 1 is shown. What is the volume of the solid formed by…

A: Let's find.

Q: Find the general antiderivative F(x) + C for the function. f(x) = 12x + 67 O 6x² + 6x + C O 6x2 +…

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Q: John and Lashonda are standing on a riverbank, 130 meters apart, at points A and B respectively.…

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Q: 1. A light hangs 15ft above a horizontal path and a man 6ft tall is walking away at 5 ft/sec. i) How…

A: According to bartleby guidelines when student post more than one question then expert must have to…

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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…

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Q: 1. Let f be a function satisfying the following properties: continuous on R\{1} • f(0) = 0 and f(3)…

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Q: Eliminate the constant 'a' from the equation (x – a)2 + y? = a² O (x? - 2y)dx + 2xydy = 0 O (x2 -…

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Q: What is the area under the graph of y = 2- x on the interval -2, 1]? X 543-2 44 1 2 4 5 O 6 13 15…

A: Find area under the graph

Q: Consider the following. u = (2, -1, 0) v = (-2, 3, 0) Find u x v. Determine if u x v is orthogonal…

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Q: Evaluate the integral. 1 (4 + r)3 dr   0

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Q: Test the series for convergence or divergence. Eh=1 n35n (n+ 2)!

A: To test the series for convergence or divergence. ∑n=1∞ n·35nn+2!

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Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

A: Differentiate R and C with respect to time .

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A: Given

Q: Sketch the region R of integration and switch the order of integration. f(x, y) dx dy 5- 5- 3 2- 1 3…

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Q: (b) f(x, y) = 3.03 + 3y2 – 4 ln y, a = 0, y = 1, dr = 0.01, dy = -0.01. since fa (x, y) = 3.3x-1+ 0…

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Q: I need some help with this question. Thank you :)

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Q: ii, Calculate the volume and surface area of a solid cylinder 1.5 m diameter and 2.5 m tall.

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Q: Find the equation of the secant line on the curve f(x) = -x²+2 passing through the points xo = -1…

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Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); fi-) U =

A: we can solve this as follows:

Q: A gardener with 600 meters of available fencing wishes to enclose a rectangular field and then…

A: Given problem:- A gardener with 600 meters of available fencing wishes to enclose a rectangular…

Q: 1. sin²(esin*r) + cos-(2t³ – 5)

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Q: Eliminate the constant 'a' from the equation. (x – a)² + y? = a² O (x? – 2y)dx + 2xydy = 0 (x² – y²…

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Q: 1 5. Find y" of y= sin 3x

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Q: Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region…

A: Given problem:-   Set up, but do not evaluate, an integral for the volume of the solid obtained by…

Q: Solve the initial value problem +3y , 0>0, y(1) = -5. de

A: To solve: θdydθ+3y = sinθθ2, θ&gt;0, yπ=-5 ⇒dydθ+3yθ = sinθθ3 This is a linear differential equation…