Test following ODES for exactness. If exact, find General solution. Do detailed Curve Sketching analysis (Domain, Intercepts, Symmetry, Asymptotes, Intervals of Increase or Decrease, Local maximum and minimum, Concavity and points of Inflection, Sketch the function/ Plot the graph) of solution. Choose value of constant of integration on your own. a. (y + 2xy³)dx + (1+ 3x²y² + x)dy = 0

Q: If f(x) = 2x + 2x – 7, find the equation of the line tangent at z = - 2. -6 Preview

A: Explanation is given below..

Q: Consider the following points. (-1, 5), (0, 0), (1, 1), (4, 58) (a) Determine the polynomial…

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Q: 2. A manufacturer wants to design an open box having a square base and a surface area of 104 square…

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Q: PART B: a) One of the submissions for the roller coaster proposal contains the following…

A: (a)

Q: 2yy" = 1 + (y')² 2

A:

Q: Find the point on the curve y = V4x + 5 which is closest to the point (7, 0). Round to at least 3…

A: Solve the a above questions

Q: The slope of the line tangent to the graph of f(x) = 15 – 3a2 at the point z = -8 %3D 48 96 O 12 O…

A: Solution is given below : Answer: 48

Q: Find the average rate of change of the function f(x) Average rate of change = Give exact answer! =…

A: Given,            The function is fx=2x2-3x+1, on the interval x ∈ 0,1.To find : Find the average…

Q: Differentiate and simplify your answer (no radicals, no negative exponents, fully factored). State…

A: Solve the following

Q: Rachel deposits $12,000 into a fixed asset account that earns 6% compounded quarterly. What is…

A: Formula:      where FV = Future Value          PV = The principal amount (the initial amount of…

Q: Find the tangent and normal lines to the curve ペー9ーチ at the Pomt (-62)

A: Given, The equation of the curve  x2-xy+y2 = 7  We have to find the equation of tangent and normal…

Q: 6. Find the derivative of y= 2x² (3x - 4). A. 6x³ - 8x² B. 18x² - 16x 7. Find the derivative:…

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Q: 4 6. ν- x3

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Q: y=x²-2xe*+2le

A: Given: y=x2ex-2xex+2ex &  Px,y=1,e  As we know that; The slope of the tangent line to the curve…

Q: Directions: Find the derivatives of each of the following funct 1. f(x) = 5x-9 %3D 2. f(x) = 4x2 +…

A: To find The derivatives of each of the given function.

Q: 1 y = ┤㈑┤慈┤

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Q: 8x 8 e Find the equation of the tangent line to the graph of f(x) = at (0, - 4). 9x -2 The equation…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.