Let g(t) be a differentiable function such that g(1)=2, g(3)=4; g'(1)=1, g'(3)=1. Let f+ df denote the differential (linear) approximation of f(1.1,2.8), where f(x.y)=x?g(x²y). Let h(x,y)=3y²+6xy+2x?. Choose the TWO correct statements below. f+df=3.7 f+df =4.9 (1,1) and (1, – 1) are local extrema of h(x,y). f+df=4.5 h(x.y) has a local minimum at (1, – 1). f+df=5.2 (1,0) and (1, – 1) are local extrema of h(x,y). h(x,y) has no local minima.

Q: y = 3e Let f(u) = 3e". Find g(x) such that y = f(g(x)). %3D u = g(x) = %D

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Q: Find y as a function of if y(0) = 18, y'(0) = 28, y'(0) = 21. y(x) = y"-9y" + 20y = 24e,

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Q: Find y as a function of a if x?y" + 15xy + 49y = 0, |3D y(1) = -5, y'(1) = 4. y =

A: Given differential equation is  x2y''+15xy'+49y=0 given y(1)=-5,y'(1)=4

Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

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Q: Find F as a function of x and evaluate it at x = 5, x = 7, and x = 9. F(x) = F(5)= F(7) = F(9) =…

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Q: 1) Find the linearization L(x) of f(x) at x = a. f(x) = 2x2 + 4x - 1, a =

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find y as a function of a if y"" - 12y" + 35y' = 24e", y(0) = 27, y'(0) = 11, y'(0) = 30. y(x) =

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Q: calculate the derivative at t = 3, assuming that rị(3) = (1, 1, 0) , r2(3) = (1, 1, 0) r{ (3) =…

A: To calculate: ddt6r1(t)-4·r2(t) at t=3, where r1(3)=<1,1,0>,…

Q: Let f(x) = e»in(²)+z² _ i) Find the x-values of the stationary points to the curve y = f(x), where 0…

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Q: Find y as a function of a if y(0) = 19, y'(0) = 26, y" (0) = 14. y(x) = y"" - 10y" + 21y' = 48e²,

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Q: Find y as a function of a if y(1) = -4, y'(1) = -9. y x²y" + 2xy' - 6y = 0,

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Q: Find y as a function of a if y(0) = 6, y'(0) = 24, y"(0) = 108. y" + 36y' = 0,

A: y′′′+36y′=0y(0)=6,y′(0)=24,y′′(0)=108.The characteristic equation…

Q: Compute the derivative for r(t) = d dt f(t) = (Use symbolic notation and fractions where needed.)…

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Q: A) Find the first and second derivatives of the function g(x) = Vx² + 2x .

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Q: 3x t²- - 1 Let F(x) = √ 12 + 1 dt. 2x (i.e. the derivative of F(x) with respect to x). What is…

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Q: Let u(t)=6t3i+t2−4j−5k and v(t)=eti+9e−tj−e9tk. Compute the derivative of the following function.…

A: solve the following

Q: Suppose f, g have the following values: f(3) = e5 and g(3) = 2. ƒ'(3) 10 and g' (3) = = 8. 4 Let y¹…

A: To find the value of y' at (3,-3).

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.