Determine the coefficients a, b, c, and d, so that the curve y = ax' + bx² + cx + d have critical point at (0, 4) and (2, 0).

Q: 1) A circular cylinder with radius r cm and heigh (a) Compute V(2, 5). (b) Find the linear…

A: Given: To explain the given statement as follows, Volume V =π r2h cm3

Q: of the form y₁ = (1+₁2+ a₂x² + 3x³ + ...) 32 = x2(1+b₁x + b₂x² + b₂x³ + ...) where T₁ > T2- Enter…

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Q: , Find two linearly independent solutions of 2a²y" – xy' + (2x +1)y = 0, x > 0 of the form Y1 = r"…

A: (Note: Please scroll to the last step for the final answer.) Given equation is 2x2y''−xy'+2x+1y=0…

Q: An object is traveling along the line y = 2x + 1 heading up and to the right. If the temperature at…

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Q: Find the line tangent to the curve x 3 + y 3 4 at the point (-3/3, –1). V3 y = 3 x – 4 V3 4 - 3 -V3…

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Q: nt) Consider the discrete-time dynamical system x1+1 = 4x,(1-x₂). If x₁ = ₁, X1+1 = Is x = an…

A: see my solution below

Q: 7. On a certain mountain range, the level is z = 1200 -0.02x² -0.04y². points north. The climber is…

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Q: Determine coefficients a and b such that p(x)=x^2+ax+b satisfies p(1)=6 and p′(1)=0

A: Since you have posted multiple question in this question which are nt interlinked so i have solved…

Q: Construct a linear system of equations to determine a quadratic polynomial p(x) = ax^2 + bx + c that…

A: Given f (x) = e^2x quadratic polynomial interpolates  f(x)   p(x) = a x2 + b x + csince p(0) = f(0)…

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: