Let f(x)=x²-3x²+6Vxe R and g(x)= max. f(t); x+1≤ t ≤ x+2,-3 ≤x≤0 1-x, Find the function g(x). x20

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Q: Solve the initial value problem below using the method of Laplace transforms. y' + 4y + 3y = - 2…

A: Solve the initial value problem below using the method of Laplace transforms.   y''+4y'+3y=-2 cos…

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Q: 1. Express f(t) in terms of the unit step function uc(t) 1, t-1, t-3, 1, f(t) = if t 5

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Q: If p(q-r) x² + q (r-p)x+r(p-q) = 0 has equal roots, then 2 1 T= 9 prove that Р + 1 r

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Q: 2. Use Laplace transform to solve the initial value problem y" + 2y + 2y = 2u3(t) (t− 3), y(0) = 0,…

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Q: Question Four (a) Verify Green’s theorem in the plane for R C (3x 2 − 8y 2 ) dx + (4y − 6xy) dy,…

A: Since you post more than one non interlinking questions, as per our guideline we can solve only…

Q: 2) a) Classify the following sequences: (i) 6.5, 9.75, 13, 16.35,........ (ii) 4 8 16 33 9' 9' 9' 9…

A: Please find the answers in next step.

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A: We know the exponential form of all the given hyperbolic functions.  Now the graph are given bellow.

Q: Question 9 A debt of $407 due in 6 months and another debt of $645 due in 9 months are both to be…

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Q: Transform: f(t) = 5t6e-4t O F(s) = O F(s) O F(s) = O F(s) = ○ F(s) = O F(s) = 30 (8+4)* 30 (8-4)…

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Q: if the tangent tangent (x117₁) to the conve of the curve again in (22, 8₂) them proustait me x 1 20…

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Q: 3.9 Obtain lower and upper bounds for Y, (G).

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Q: Sum of first four terms of the appropriate Fourier series of f(x) = 3,- π<x<0 -3,0< x < π T at X =…

A: Given,               f(x)=3,-π&lt;x&lt;0-3,   0≤x≤π, at x=π2.

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Q: minimize x2 - (x₁ - 2)³ + 3 subject to x₁-x₂² - 4 ≥0, x1 - 10 ≤ 0.

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Q: 2F. n 1 ;;1=2" (b), (26)

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Q: Find a quadratic equation whose product of roots x₁ and x₂ is X1 x2 equal to 4 and satisfying the…

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Q: Consider a word COMMITTEE (a)    How many distinguishable orderings of the letters from the word…

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Q: (a) Show that for each complex number z ‡ 1, (b) Show that (c) Show that η n Στ k=0 Text Σcos(k0)…

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Q: The sconomy of a small island nation is based on two seciors, agrioulture and tourism. Production of…

A: Given that the economy of a small island nation is based on two sectors, agriculture and tourism.…

Q: 7. (Solve a simpler case or similar problem then look for a pattern) Find the last digit of the sum…

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Q: Which one of the following is NOT equivalent to pq? A. (~pVq) ^ (pV ~ q) B. (~pVq) ^ (q→ p) C.…

A: The truth table of some of the standard statement is  p q p∨q p∧q p→q p↔q ~p     T T T T T T F…

Q: non-negative continuous function. 5 п 3 Let f(x), x 20, be a If f'(x) cos x ≤ f(x) sin x, V x ≥ 0,…

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Q: Evaluate each integral. *x+y ["ya [ y dz = *x+y [*** Jx-y y dz dy = • JL.Y [y dV, where E = {(x, y,…

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Q: Find the coordinate vector of v relative to the basis S V= (14, 6, 24); V₁ = (4, 0, 0), v₂ = (6, 6,…

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Q: Prove or disprove: ne N. If lim xn exists. Let m≥ 2, and let n, yn E Rm for all 0 and lim(rn yn)…

A: Here we take counter example for disprove given statement

Q: Consider the solid λ bounded by the xz-plane, the yz-plane, the plane z = -1, the plane x+y = 3, and…

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Q: Q1- If z₁ =3+2i, and z2 = 1-2i. Fined the real part and imaginary part of the 2z2-z₁+5-i following…

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Q: Let f (x) and g(x) be differentiable functions in (a, continuous at a and b, and g(x) #0 in [a, b].…

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Q: In step 2, how did you get the third part where it says limit 2^(n-1) x theta x sin(2^(-n)theta) as…

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Q: (2x-3, 1≤x≤3 eal value of b such that f(x) has the smallest value at x =

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Q: 7. Use a double integral in polar coordinates to find the area of the region inside both the…

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Q: Transform: f(t) = 4t² sinh5t O F(s) = O F(s) = O F(s): OF(s) = O F(s) = OF(s) = O F(s) = O F(s) = =…

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Q: An urn contains five balls numbered 1, 2, 2, 8, and 8. If a person selects a set of three balls at…

A: Given an urn contains five balls numbered 1, 2, 2, 8,and 8. X 1 2 8 PX 15 25 25 The expected…

Q: The temperature at point (x,y) on a metal plate is T(x,y) = 64x² − 64xy + 16y². An ant on the plate…

A: Given that the temperature at the point x, y on a metal plate is                               T(x,…

Q: Find the mean and standard deviation of a normal distribution that approximates the binomial…

A: Given n=200, p=0.25 (46)  x =np    =200×0.25    =50∴x =50 (47) σ=np1-p  =2000.251-0.25 =6004  =6.12

Q: If F(s) = -3s² s + 1 is the Laplace transform of f(t), find the following, correct to three decimal…

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Q: f(x) = 3x4 + 2x³ − 10x² − 5x + 20

A: Regular-Falsi Method: Find points x0 and x1 such that x0&lt;x1 and fx0·fx1&lt;0. Then, take the…

Q: A cereal manufacturer wishes to produce 1000 pounds of a cereal that contains exactly 10% fiber, 2%…

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