Solve the differential equation by variation of parameters. y" + 2y' + y = e-t In(t) y(t) =

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A: We will find the slope

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A: Given that y=sinπx+4bounded by x=0,x=2 and y=0Solutiuon :centroid x¯…

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A: NOTE: Refresh your page if you can't see any equations. . properties of logarithms are

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A: The given integral ∫x3ex4dx

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A: Topic:- application of derivatives

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A: The side of the square = L  let the length of the square = x,

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A: This question can be solved using the concept of differential equation.

Q: Use sigma notation to write the sum. 4 4 1 + 2 1 + 3 4 1 + 1 + + + ... + 4 1 + 19

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Q: We have found the following Wronskians. W = −e-³x; W₁ = −e-²x (4 + ex)-¹; W₂ = e¯x(4+ e*)-¹ Р We…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: 15) I What is the average rate of change of f(x) = from x = -2 tox = 4? x-s X+3 b 24 7 M C. d. 25 21…

A: We know that the expression for the average rate of change between the interval x2≤x≤x1 is: Average…

Q: 1 if x > 0 x²-1 if x ≤0 g(x)=x-1

A: Given the function, gx=1x-1if x>0x2-1if x≤0

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In√√x² + y2, (3,…

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Q: 2 Solve the following ODES by 1.2 • ý -2y +y = e sinx Inverse Operator method X X Anse y=cie +…

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Q: all company of science writers found that its rate of profit (in thousands of dollars) after t years…

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Q: The graph below is the function f(x) -4 -3 -2 -1 8-1 lim 24-2 4 3 2 1 Determine the following…

A: Solution: As we can see in the graph

Q: Find the general solution of the given higher-order differential equation. + 3y" + 3y' + y = 0

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Q: What is ette-t At- ○ - In [e* O ○ ○ dx e* + C] In [e* + e* + C In [e* e*] + C -In [ee] + C

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. x+y+z= 12, (4, 3, 5)…

A: Our Aim is to find :-(a) An equation of the tangent plane to the surface at the given point.Here…

Q: (a) Determine whether the series n=1 n+1 n³ +3 is convergent or divergent.

A: Solution: ∑n=1∞n+1n3+3

Q: Find the domain of the function. 7 |x²-161 g(x)

A: Domain : It is the set of all real numbers for which the equation is defined.

Q: Find the critical numbers for h(x)=x^2-x^4. Show all work.

A: The objective of the question is determine all the critical point of the given function.

Q: 1 For the parametric curve * = find an equation for the tangent line to the curve at the point…

A: To find equation of tangent line:

Q: Find f(x,y) and fy(x,y). Then find fx (2, -1) and fy (-4,3). f(x,y) = In 5x4 +8x²y²| fx(x,y)=…

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Q: If In a = 2, ln b = 3, and ln c = 5, evaluate the following: a² b²c4 (a) In = (b) In √a²b²c4 =

A: To evaluate the given expression.

Q: 4. Condense the log to a single log expression. a. 2 log y - 3 log x - 2 log 10 b. Ina+3 ln y

A: See this solution in below

Q: Find a parabolic curve that would fit the following data. Let  y = a + bx + cx2. x      3    5…

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Q: cook Use the power series f(x) = In (1-x) = - Σ for -15 x <1, to find the power series…

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Q: Find the gradient of the function at the given point. f(x, y) = 4x + 2y² + 4, (1, 2) Vf(1, 2) =

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Q: Use left and right endpoints and the given number of rectangles to find two approximations of the…

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Q: Write an equation for the function graphed below 5+ 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 y = -5+ 1…

A: topic- graph of a function

Q: 2) Evaluate √3|x + + 1| dx

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Q: The dose-response curve for x grams of a drug is f(x) = 8(x − 1)³ + 8 for x ≥ 0. (a) Make sign…

A: The solution is given below

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Q: a. b. algal dy dx dy dx + y = xy³ - y = ex y² -X

A: See this solution in below.

Q: What is the domain of the reciprocal function of f(x) = 5x+1? {x € R\x2} c. b. (x=Rxs-) a. d. {x =R…

A: We can answer the question as below.

Q: -4 -2 (a) x=¹t+3, y = 2² VX (b)x=²2t, y = √t 11 (c) x = ²³ - 2t, y = 2² - t ✓X III (d) x = cos(5t),…

A: Please see the below picture for detailed solution.

Q: 1 Q BAS 6 2 [//dx Which of the following is the integrand in the definite integral above? Select the…

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Q: Integrate using the fundamental theorem of calculus

A: Our Aim is to evaluate the integral given below using Fundamental Theoem of Calculus.∫01x4+12 dx…

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Q: The top of a ladder that is 5 m long slides down a vertical wall at a rate of 2 m/s. At what rate…

A: Given :Length of ledder=5m