4x-x² Given the rational function r(x)= x²-4 (a) Find all intercepts and asymptotes of r. (b) Describe the behavior near Vertical asymptotes. (c) Sketch the graph of r in interval [-8, 8]. Show clearly x- and y-intercepts, and ALL asymptotes. (d) What is the y-intercept of the graph?

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A: Follow these steps.

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A: Problem is solved using concept of second-order Adams-Bashsorth Method.

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A: Here we using integration w.r.t to x and y to find this

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A: This is a problem of the set theory.

Q: 2.4.3 Find the value of X(0.3) for the initial-value problem d²x 2 dx + x = sint, x(0) = 0, dx (0) =…

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Q: Q4) Find the root of f(x)= (x^2)-5, in interval [0,4] by using bisection method.

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Q: 1. Use the Modified Euler's method to find y when x = 0.1 to 0.2 given that = dy dx √x + y for y(0)…

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A: This is a problem of Logic.

Q: 6. Consider [n] := {1,2,3,...,n}. The uniform subset graph U(n, k, i) has vertex- set the k-subsets…

A: Given: The set, n:=1,2,3,...,n. The uniform subset graph Un,k,i has vertex set the k-subsets of n.…

Q: (0) = 6, y'(0)

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A: Use the given information.

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Q: 1. Use the Modified Euler's method to find y when x = dy 0.1 to 0.2 given that = √√x + y for y(0) =…

A: Modified Euler's method uses the formula: ym+1=ym+hf(xm+12h,ym+12hf(xm,ym)) to perform the…

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A: Ans 5 True Yes, since the set of real numbers can be expressed as a countable union of closed sets.…

Q: (B) Use Tabular integration f(t³-4t² to evaluate the following: - + 5t+32) sin(t)dt

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Q: f(x) = { ₁ Sketch the odd periodic extension of f. 1 0<x< π/2 π/2<x<n.

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Q: find solution using direct integral method for the partial differential equation below: J³Z 1 = 12…

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Q: 3. A wildlife manager counted 1800 mice in a 10-km² area of forest. It is predicted that the mouse…

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Q: Solve the following non-linear equations: 2 100x₁ - 10x₂² + 5x3³ = 70 3x₁² + 10x₂-X₁X3 = 5 X₁X₂ +…

A: Thank you for the question. According to our guidelines we can answer only  first question and…

Q: 5. y + 4y = sin x + 3 cos x Ans: y = C₁ + C₂ cos 2x + C3 sin 2x + sinx-cosx

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A: False.

Q: Q2: (B) let y = 3sin5x-2cos5x show that y + 25y = 0

A: given y=3sin5x-2cos5x find the derivative y'=35cos5x+25sin5x=15 cos 5x+10 sin 5x…

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A: 1l

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Q: 5. The dimensions of a cylindrical object are increased by a scale factor of 3. The volume of the…

A: A cylindrical object will have radius r and height h. Volume V = πr2h . After scaling the radius is…

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A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

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Q: (B) Use Tabular integration to evaluate the following: - f(t³-4t² + 5t+ 32) sin(t)dt

A: The solution of the given problem is below, using tabular integration...

Q: (B) let y = 3sin5x-2cos5x show that y + 25y = 0

A: Here we use basic differentiation to prove this