Find the limit or show that it does not exist. lim x - √x 818

Q: Solve the following Differential Equations with Laplace Transforms y" - 6y' + 15y = 2 sin(3t), y (0)…

A: Let's solve diffrential equation by using laplace transform.

Q: 2. Brine containing 3 lb/gal of salt enters a large tank at the rate of 2 gal/min and the mixture…

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Q: x+3 x ³ + 8x² +16x S da

A: To evaluate the given integral by using partial fractions.∫x+3x3+8x2+16x dx

Q: 5) An isotope of lead decays according to the function remaining, in grams, after t minutes. a) What…

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Q: Q2) Determine using Cauchy Riemann equations the function below is analytic or not? f(2)=x² +…

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Q: 2x³ − 45x² + 300x + 6 has one The function f(x) = 2x³ local minimum and one local maximum. This…

A: Given: Axis interception points of 2x3-45x2+300x+6:  X Intercepts: -0.01994…, 0, Y Intercepts: 0,…

Q: 13. Determine the distance between the following lines. [x, y, z]= [4,5,9]+s[-3,4,-9] and [x, y, z]=…

A: Above question is solved.

Q: Q1) L-1 1 s(s²-1)/ a) cosht-1 b) 1-cosht c) (cosh2t - 1) d)/(1-cosh2t) Q2) The general solution of…

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Q: *2t-h 5 if t=2 then h = -1 true O false O

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Q: Find the critical values (if any) of the given functions. With solution please.

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Q: APPLICATION OF 1st ORDER DIFFERENTIAL EQUATIONS 1. Brine containing 3 lb/gal of salt enters a large…

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Q: Find the area common to the circle r = 3 and the cardioid r = = 3(1 - cos 0)

A: Figure of area enclosed by both curve÷

Q: r H+ sin x sin 2x dx 2 cos X

A: Solving the problem by finding the value of the integration.

Q: If X(z) is the z-transform of the signal x(n), then what is the z- ?transform of the signal x(-n) x…

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Q: Determine the following derivative with respect to x: Y = cos(sin(cos x))

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Q: The force of magnitude F-108 lb acts along the edge of the triangular plate. Determine the moment of…

A: We have to find moment value for the given force.

Q: Find the acceleration u= 2x² + 3y, v=- - 2xy + 3y² + 3zy, Example the following flow field: W =- at…

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Q: *.The equation (y"+x3y'+y=sinx)is.............. differential equation Linear,2nd order, Homogenous O…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find y': y = cot 0 sin 0 O sin² 0 1-tan²0 O1+sin² 0 cos³0 O-1-cos² e sin³0 3

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Q: Show that: le a (i) a е a а al (2a +1)(1-a)2

A: Given :laaalaaal=2a+ll-a2

Q: 2.2 2.3 Determine whether the series below converges or diverges. Determine the first four terms in…

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Q: Solve the following Differential Equations with Laplace Transforms y" - 6y' + 15y = 2 sin(3t), y (0)…

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Q: S dy ² + 4y+20) ²

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Q: ל 15 18 a = (3₂16) 6= (-2,0,1) → 08 -> 2² = ²²-23 +5k →> oc CẢ OA

A: Given :a→=3,1,6=OA→b→=-2,0,1=OB→c→=i-2j+5k=1,-2,5=OC→

Q: a b 3. Write the scalar equation of the plane with normal vector = [5,-1,-2] and passing through the…

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Q: t b) tz 16) L-¹ (5-3)²+25) = c) tz estsinst a) 5 d) t est sin3t 5 b) c) e-at sin3t 5 eatsinst d)

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Q: 2y V. Consider the lines : x + 1 5 = = 2z - 6 and m: x = −1+10t, y = 7t, z = 2 + t. 7 1. Determine…

A: As per our guidelines we can answer only one question so kindly repost the remaining questions…

Q: dh dt k √h(t) ||| h(0) = 2 2 ● T.V

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Q: Solve the following equations 2)3x+2 = 27 1) 2Ln(√x + 3) + 2Ln(√x-1)=Ln(6x-7) I 1 1

A: Let's solve both equation.

Q: 1. Consider the function y = ex²-3x+1. Find the extreme value of the function (classify as minimum…

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Q: Find the limit or show that it does not exist. √x+3x² lim 818 4x - 1

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Q: X5 x3 +4 +4 dx

A: WE can find the integration as below.

Q: Let a = and b = . Find - à - b.

A: Given :a→=5, -5, -1b→=-4, 4, 0

Q: integrate [(x csc^2 (2x) - x cos (2x)] dx

A: Given problem:-  ∫ [(x csc2(2x) - xcos(2x)] dx

Q: Q9) The linear form of nonlinear ODE y' - 2y = 2y, is: b) u' - 6u = -6 a) u' + 6u =-6 c) u' - 6u = 6…

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Q: Differentiate f(x) = (a-x)(a + x) with respect to x. Assume that a is a positive constant. f'(x) =

A: Solving the problem by finding the value of the differentiation.

Q: | 1) 2Ln(√x + 3) + 2Ln(√x − 1) = Ln(6x - 7) 2)3x+2 = 27

A: This question is related to solution of equations, we will solve it using given information.

Q: 2. Find d using implicit differentiation. Enclose final answers. dx (a) √x=y=√√√x + y = 5 (b) xsin y…

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Q: Find the arclength of the curve y = 3x² + 5 on [0,3].

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Q: Question 4 (a) Solve the following: [²4x¹dx (b) Explain with the aid of a sketch how this value can…

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Q: Solve the following Differential Equations with Laplace Transforms y" - 6y' + 15y = 2 sin(3t), y (0)…

A: Let's solve diffrential equation by using laplace transform.

Q: H.W: show that the equations are homogeneous and solve: 20 2. x² dy + (y² - xy)dx = 0

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Q: A piece of cardboard measuring 14 inches by 9 inches is formed into an open-top box by cutting…

A: Given :  A piece of cardboard measuring 14 inches by 9 inches is formed into anopen-top box by…

Q: 5. Find the length of the curve = = = (1 ²+2) X=- 3 9 0≤ y ≤ 4

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Q: Determine the critical point/s of f(x) = ln(x² + 4x + 14) on [-4,2]. 0x= -3 Ox=1 0 x = 0. 0x = -2

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Q: The function f(x) 2x³ = local minimum and one local maximum. This function has a local minimum at x…

A: The given function:fx=2x3-45x2+300x+6.We need to find its local minimum and local maximum.

Q: Determine using Cauchy Riemann equations the function below is analytic or not? f(2)=x² + y² - 2xy

A: This question can be solved using the concept of the two conditions of Cauchy Reimann for a function…

Q: 4x* dx

A: We need to solve the following. So,            ∫-224x4dx=4·∫-22x4dx=4x55-22=4·645=2565

Q: A giant spherical-shaped snowball is melting. If the radius decreases at the rate of 0.5 in/min, now…

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Q: Assume that the number of bacteria R(t) (in millions) present in a certain culture at time t (in…

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