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Q: Find in the parametric equation d'y dx² x = 5 sin² t y = 2 cost 0≤t≤ 2π.

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Q: - Solve the linear ODE using an Integrating Factor. x². dy dx + 2xy = 3sin(8x)

A: solution is given below

Q: Determine the area of the region bounded by x=3+y^2, x=2-y^2, y=1 and y=-2. *

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Q: The rate of a continuous money flow starts at $600 and increases exponentially at 2% per year for 15…

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Q: On the Illinois state tax form, numbers are to be rounded to the nearest dollar. If Heat earned…

A: If you have to round off to complete integer then we need to look the first number after decimal.

Q: 1) If y = (x − a)√2ax - x² + a² sin−¹(*—ª),t ), then y'= 2√2ax-x² a is constant.

A: As per instructions, Here is the answer of question 1

Q: with this can you solve D and E with this information. Thanks.

A: Given problem:- D) Use the First or Second derivative test to prove that there is a relative minimum…

Q: Calculate the gradient of f(x, y) = sin(x² - y) Vf=

A: Finding the partial derivative of the function.

Q: Use implicit differentiation to determine the derivative of: tan² (xy² + y) = 2x.

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Q: of the points where the parametric equation y = 2 cost 0≤t≤ 2π will have vertical tangent. Determine…

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Q: The integral of sin x³ dx is cos x + Option 1 cos³ x 3 + C cos x + Option 2 cos² x 2 + C

A: Given ∫(sinx)3dx=∫sin3xdx

Q: a. Write the equation of the line that represents the linear approximation to the following function…

A: Concept: Linear approximation: Approximating the value of a function at a point with a line is known…

Q: Evaluate the following: fo(5x²y³ + 3x) dydx a. b. ff ex+ydA where R = {(x,y)|-x≤ y ≤x, 0≤x≤ 2}

A: To find the value of given double integrals.

Q: 1. Find the Inverse Laplace Transforms of the following. 3) 3s³+3s 56

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Q: P 2. ( Use the disk or washer method to find the volume of the solid obtained by rotating the region…

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Q: For the function f(x) = 2x², make a table of slopes of secant lines and make a conjecture about the…

A: Slope= df/dx

Q: Consider the position function s(t)= - 16t+96t representing the position of an object moving…

A: Given problem:- Consider the position function s(t) = - 16t2 + 96t representing the position of an…

Q: Convert the rectangular coordinates (5,-5√3) to polar form. Letr> 0and 0 <0<2TT.

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Q: Determine the volume produced by the region bordered by 32 IT 15 "1 x² - 4x - 4y + 4 = 0 and y = 1…

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Q: Find the volume of the solid generated by revolving the region bounded by the lines and curves y =…

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Q: Consider the general solution of a differential equation is y=C₁x-C₂ ln x² find C₁ and C₂ when…

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Q: ||. Minor and Cofactor 1. Find the cofactor of 6 in matrix D 9 8 4 2 7 -9 3 4 D = 6 -3 2 3 8 9 3 2 ㅋ

A: Let's find cofactor of 6 in matrix D.

Q: 3. You are tasked with designing a cylindrical can. The material for the top and bottom of the can…

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Q: 3z (1-4z-2z²)² dz

A: Given, ∫3z1-4z-2z22dz Formulas used: ∫xndx=xn+1n+1∫1xdx=lnx

Q: Given that Inx+3 f(x) = 3lnx-1 Find the formula for f−¹(x). State the domain of f−¹(x). Show all…

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Q: The ellipse + 1 can be drawn with parametric equations where (t) is written in the form 4²2 r(t) = r…

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Q: Inys 5. lim y→⁰⁰ y

A: To solve for the limits of the following function using L'hospital's rule.limy→∞ ln y5y

Q: 3. Use the cross product properties to prove the relation (a - b) × (â+b) = 2(â × b) given a = (1,…

A: Given,a=i-3j+2kb=-2i+0j+k

Q: n=1 n 2n+1 2n-1 xch

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Q: If f (x) = x(x - 1)³, then which of the following statements is correct? f(x) has a maximum point at…

A: We have to select the correct statement from the given statements.

Q: Evaluate 0-2²-²4 where is a unit cele centered at the origin

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Q: The given definite integral is equal to x3 dx Jo x + 1 O 1.23 O 0.43 O 0.18 O 1.42 Onone of the…

A: The given integral:∫01x3x+1We need to evaluate the definite integral.

Q: x'dx √√x(1-x)

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Q: A cylindrical can without a lid is to be constructed to contain 800 ml of liquid. Determine the…

A: This question can be solved using the concept of maxima and minima.

Q: b.) xyz dv if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

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Q: 1 2 In|2|

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Q: 2. -4 1 3 -3

A: to evaluate: -431-3

Q: If f(x)=5x(sinx+cosx), find f′(x) =

A: Product Rule of differentiation : du.vdx=u.dvdx +dudx.v dxndx=n.xn-1 dsin(x)dx=cos(x)  and…

Q: (-2,5,7) + t(-3, 1,-4) and that the point Given a line defined by the equation T = P(x, y, 15) lies…

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Q: n Express the function n, lim 21³ n→+∞ n5 i=1 and then find the limit. in closed form

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Q: (a) Solve the first order linear ordinary differential equation x sin x + (sin x + x cos x) y = xe…

A: As per bartleby guidelines we only give first question answers.

Q: 6.) I. Simplify. Write "undefined" for expressions that are undefin -3 -6 -2 6 619 1 4 -4 -4

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Q: Find the volume of the solid obtained by rotating about the axis the regi and bounded by y=2x²) Y=o…

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Q: TRUE or FALSE: 1. The integer 5047 is a prime numbe

A: To write down that the given number is a primer number or not.

Q: Find the average value of the function on the given interval. f(x)=x²-7: [0, 1] Set up the integral…

A: Average value of a function f(x) on [a,b] is given by, V=1b-a∫abf(x)dx

Q: 4. tan(5) a. Find the exact value for: b. Solve for x: tan(2x) = √3, xe [-]

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Q: consider the function y=−3sin(4x−π/2)+1  a) What is the amplitude? b) What is the period?  c)…

A: Disclaimer:  “Since you have posted a question with multiple sub-parts, we will solve the first…

Q: The graph of a function y = f(x) on the interval [ - 3, oo) is shown below. Use the graph to answer…

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Q: 54. Look for the volume of the solid produced by rotating the region enclosed by 1792# T y - x² =…

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Q: B. Find the slope of the curve at the given point. 16. 2x²-3x+1 at (2, 3) 17. =3x²-2x+1 at (-1,6)…

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