Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. Point (0, 0) f'(0) = Function f(0) = 6 sin 0 - 0,

Q: Use the Laplace transform to solve the following initial value problem: y' + 7y - 18y=0 y(0) = 1,…

A: As per guidelines, I can answer maximum three sub parts of a question. Since you have asked for…

Q: 4 cos x -dx 1+ cos x

A: Our Aim is to evaluate the integral given below:-∫cos4 (x)1+cos (x) dx -(i)

Q: = If cot(x) Give exact answers. sin (²) cos (77) tan(72) = 18 5 = Submit Question (in Quadrant 2),…

A: I am attaching image so that you understand each and every step.

Q: 2. Find the area enclosed by T = @ cos 30-

A: We need to find area.

Q: 2x-4 x²-4x+3 1. Express the function f(x) fractions. Find the interval of convergence. = as the sum…

A: Here, the given function is: f(x)=2x-4x2-4x+3

Q: Evaluate the following integral: sos X 1 +1 d dydx

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Q: A curve is defined implicitly by the equation x² + 3xy + y² = 1 Differentiate implicitly to find dy…

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Q: The rate of change of the population of animals is proportional to the population at a given time.…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Three sides of a rectangular playing field are to be fenced with 400 m of fencing. Determine the…

A: Application of derivative

Q: Evaluate f2Tof 1 0 rdrde

A: The given integral is: I=∫02π∫01rdrdθ   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 And…

Q: Find the volume of a pyramid with height 29 and rectangular base with dimensions 6 and 9 using…

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Q: Given the vector field F(x,y) = [x/((x^+y^2)^(3/2)), y/((x^+y^2)^(3/2))], Find a fucntion f(x,y)…

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Q: (D²+4D+5)y=35e : y(0)--3, y'(0)-1

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Q: Find f'(x) and f'(c). f(x) = (x5 + 5x)(3x5 + 5x - 2), c = 0 f'(x) = f'(c) =

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Q: s²+1 Find the inverse of Laplace transform of log (² (s−1)²,

A: =L^-1[log(s^2+1/((s-1)^2) =2(e^t-cos(t))/t

Q: 10. Consider the piecewise function (with the piecewise having TWO pieces). Find the piecewise…

A: We need to find piecewise function.

Q: Evaluate f(x, y, z) ds. f(x, y, z) = x² + y² + z² S: z = x + y, x² + y² ≤ 1

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Q: maximum

A: if you specifically asking to how to find maximum and minimum value. Please refer to the image below…

Q: Show in paper. Find the integral of (2xcot(x) csc²(x)) dx.

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: Determine the points at which the graph of the function has a horizontal tangent line. x² f(x) x-3…

A: Given:      fx=x2x-3 A point on a function will have a horizontal tangent line where the first…

Q: A company determines that its weekly online sales, S(t), in hundreds of dollars, t weeks after…

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Q: Let f be the function defined by f(x) = sin 2x + cos 7x and let g be the function defined by g(u) =…

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Q: A curve is defined implicitly by the equation ax+by² = p.2 Given that a=27, b=-4 and r=3, find the…

A: Given problem:- A curve is defined implicitly by the equationax+by2 = r2Given that a=27, b=-4 and…

Q: Consider the following. u = 3i + 3j v = -3i+j+ 5k Find u x v. Determine if u x v is orthogonal to…

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Q: Situation: An online retail company tracked total number of purchases monthly. In February 2007 they…

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Q: Problem 17. Suppose that F(x) = = [₁,²50 Find F"(2). f(t) dt, where f(t) = 1 ² √² + 1² VT U - du.

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Q: 2).  Consider the logistic equation in the form P'(t) = CP − P2. Solve the logistic equation for C =…

A: Given problem:- Consider the logistic equation in the form P'(t) = CP − P2. Solve the logistic…

Q: If the rate of change in the microwave rays M(x), where x is the distance, decreases with a rate…

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Q: 5 1 So (125 + 25x + 6) dx 6o S X (1 + x²)3 dx / 1 + x² dx 1

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Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

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Q: Find the indefinite integral. (Remember to use absolute values where appropriate.) 1 / +5/9(7 +…

A: ∫1x897+x19dx

Q: Suppose at 10n and n(1) = -2. Answer the following. 8) Separate the differential equation, then…

A: Topic:- application of integration and differential equations     Note:- as per our guideline if…

Q: For the following equations, enter y if the equation defines y as a function of a but not vice…

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Q: 55. Find the area bounded by r = 4 sin 20 a. a. 4n square units b. 8n square units C d. 4 square…

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Q: 12. Find the radius and interval of convergence of the power series ∞ n=1 (x-4)" √√3n

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Q: Question 3 Given the following, complete the questions below: A= B= 2 a. Perform the transposition…

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

Q: Find all cube roots of the complex number −1 + i

A: We have to find all the cube roots of the given complex number.

Q: Given the initial condition y(0) = 2, find the particular solution of the equation exy' - 2x = 0…

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Q: 17. Find the linear function f(x) that is parallel to 4x + 3y = 6, such that f(0) = 7.

A: Given function, 4x+3y=6, That is 3y=-4x+6 y=-43x+2 compare to y=mx+c Therefore m=-43

Q: 45. Which of the following is the Laplace transform of cos(2t)+2tsin(2t)? a. s^2/(s^2+4)^2 b.…

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Q: -4 -3 -2 M lowest = middle = highest = 2 N H 1 2 For the above rational function f( x ) = 16x 4x² +…

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Q: Which of the following series should be used to determine the divergence of the series Σ, V5n2+2n+4…

A: Given :- ∑n=1∞5n2+2n+4n

Q: 2 i) [x² ( x + ²7 - 2²/1) dx x i) Ï 0 x³ - 8 x-2 dx ii) ii) f (x³ + 3x² + 1) e-2x dx xe xe1+x dx

A: Given:   i) ∫x3x+2x-1x2dx Expand   =∫x4+2x2-xdx Apply linearity     =∫x4dx+∫2x2dx-∫xdx

Q: The area of a square with sides of length s is given by A = s². Find the rate of change of the area…

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Q: A region bounded by fly) = 5 - y, y = 1, y = 4, and x = 0 is shown below. Find the volume of the…

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Q: t is a fact that the function  f(x) = x(161/x − 1) has a limiting value. Use a table of values to…

A: We need to find limiting value.

Q: Consider the function f(x) = 12x5 + 15x¹ - 240x³ +2. f(x) has inflection points at (reading from…

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Q: a and d needs a solution

A: This question is related to Laplace transform and differential equations, we will solve it using…

Q: 3x2+2 0 2x²+4x+3 So dx

A: