Fix a constant r>1 Using the Mean Value Theorem that enx > 1 + x for any fixed x >0 prove

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Q: 15.a Is the function a.EVEN b. ODD f(x) = |x|, -π< x < T

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Q: 2. Evaluate the double integral that will find the volume of a solid bounded by =1-2y²-3r² and the…

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Q: Prove by Mathematical Induction that: 1∙1! +2∙2!+ +...+n∙n!= (n + 1)! –1

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Q: 4. Given the matrix C = 463 9 -2 5 5 1 12 48 -3 find bases for both the row space and column space…

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Q: Compute the orthogonal projection of = 3 onto the line L through -2 and the origin 2 proj, (v) =

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Q: 4. The boundary of a field is a right triangle with a straight stream along its hypotenuse and with…

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Q: = ²/² (e ² + e²^²) 3. Obtain the Maclaurin series for cosh x using the fact that cosh x =

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Q: 5. L-1 wcose+ssine s²+w² a. sin (wt + 0) b. sin (t + 0) c. cos (wt + 0) d. cos (t + 0) }, w & 0 are…

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Q: Give two sets that are equal. Prove that they are indeed equal by using the "Axiom of…

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Q: 2. SET-UP the definite integral that will give the area of the region specified using (a) x as the…

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Q: tips, and rates to help you save money on utilities 1. a) What are the beginning and end dates of…

A: Beginning date  is May 12, 2020 see the top left corner

Q: 1. A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

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Q: What is the y=x^2 4 and O 1/4 01/2 1 3/2 Ο ΝΑ x-coordinate of the centroid of the plane region…

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Q: Follow the instructions below: a. Use Laplace transforms to solve the following Differential…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: A = -2 - D = 3 0 B 2 " 2 13 3 E = SHE 5 > 4 5 -2 -4 31 -2 3 2 2 5 0 -4 -4 5 3 -4 -4 0 -3 2 3 - 7.…

A: Let us find the inverse of the matrix E and and answer the questions from 7 to 10 regarding its…

Q: 1. An open box is to be made from a 20-inch by 32-inch piece of cardboard by cutting out x-inch by…

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Q: A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant…

A: Radius increase at constant rate of 3ft/s . Hence radius after t second is given by  r(t)= 3t. Area…

Q: Find (if possible) the two linearly independent solution series for the equation: xy" − y' + 4x³y =…

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Q: 1 £{sin?;nt} 2

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Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^2 + 1,…

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Q: L{5cosh2t-3sinht} 1. 5s 3 a. s²-4 s²-1 3 5s b. s²+4 s²-1 3 5s C. s²-4 s²+1 5s 3 d. s²-4 s²-1 - +

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Q: 2. Using power series, evaluate lim x →0 sin x-x 3 x

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Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15 cm/min.…

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Q: _ƒ(t) = {to 0, 0<t<π π < t < 2𠂃(t + 2π) = f(t).

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Q: y-coordinate of the centroid of the plane region bounded by 22 What is the y = 2x + 1, x + y = 7,…

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Q: 9)THE ELEPHANTS Recently, a study on the African and Asian elephant populations was published. The…

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Q: 1. In solving the beam equation, you determined that the general solution is Nếu đi y 9₁x³ + tốt…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Given A = 6 " 1 2 1-3 19 (a) Is b in col(A)? Explain. (b) Set up and solve the normal equations to…

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Q: Find the Fourier sine series expansion and Fourier series expansion, respectively, for f(x)=(5,0524²…

A: Note: As you highlighted the specific subpart of the question so I answered here only that part.

Q: What is the volume in cubic units of the solid formed when the region bounded by y = 2x + 1, x-axis,…

A: This is a problem of the volume of rotation.

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Q: 4. Use the method of undetermined coefficients to find a general solution of the equation y" - 2y" -…

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Q: Referring to Figure 11, suppose that fr F-ds=4n, fo F.ds = 4T Use Green's Theorem to determine the…

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Q: 1. Evaluate y'+3y²+2y=e-t , y(0)=4, y'(0)=5

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Q: Describe the level curves of f(x, y) = x + 2y Sketch the level curves for c = ±1, ±2, ±3, ±4.

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Q: At a local market place, Naomi had 510 dolls to sell. In the morning, Naomi sold 160 dolls. In the…

A: Seven Thousandths = 0.007   Total dolls Naomi had = 510 Total dolls sold = 160 + 117 +100…

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A: First we will know that , what is Combination and Permutation. A Combination is Selection of items…

Q: Identify the graph of the function below: * n= x, 0<x<T = π, π < x < 2π, f(x) -2π O & @ # f(x) +3π…

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Q: 10. y" + 3y + 2.25y = 9t³ + 64, y(0) = 1, y'(0) = 31.5

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Q: 3. Solve by using Laplace transform where y" + 4y = f(t) f(t) = y(0) = 0, y'(0) = -1 [ 1 0 < t < 1 0…

A: solution :

Q: Find the Laplace transform of f(t) = = {/5/2 {1/2_3++3 0 ≤ t < (2 + 1) t≥ (2+1)

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Q: Consider the following IVP: y" - 3y' - 10y = 1, y(0) = -1, y'(0) = 2 (a) Find the Laplace transform…

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Q: - Using Limit Comparison Test show that this series converges when x = -2.

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Q: Let V be a unitary space and a, b of V unit vectors for which (a, b): 1/4 (1 + i); Then the norm of…

A: Given : V is a unitary space and a, b∈V are unit vectors for which        a, b=141+i To find : a-2b…