dx 8y – x² – 12 dt - | dy - 2(x – 2)(y – 6) dt (a) Does there exist a yo > 0 such that if x(0) > 0 and y(0) > yo, then y(t) > yo for all t > 0? If so, give such a yo and explain briefly. If not, justify your answer.

Q: | f(t) dt =xarctan x

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Q: Let h(x) = f(x)g(x). If f(x) = 4x² – 3x and g(x) = In(3x – 1), what is h' (x)? Select the correct…

A: The given functions are fx=4x2-3x and gx=ln3x-1. Here,  hx=4x2-3xln3x-1.

Q: 4x-y<-1

A: Given  4x-y&lt;1 Can be rewritten as y&gt;4x-1 So we take the area above the line y = 4x -1 And all…

Q: Find a general solution of (D² +4)(D – 1)(D + 3)²y(x) = 0. 1. D shows the derivative operator.

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Q: 25 Suppose that X₁ and X₂ have a joint pdf f(x₁, x₂) = (2/3)(x₁ + 1), for 0 < x₁ < 1,0 < x₂ < 1,

A: Given function, fx1,x2=23x1+1 0&lt;x1&lt;1, 0&lt;x2&lt;1 Consider, the pdf for X1, fX1=∫x2fx1,x2dx2…

Q: Find the linearization L(x) of f(x) at x = a. f(x)=x+, a= 2 3 O A. L(x)=x+1 3 2 23 OB. L(x)= x+3 5…

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Q: Let g(x) = = f(t) dt, where f is the function whose graph is shown. = 8 6 4 2 -2 -4 2 4 f 00 8 (a)…

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Q: Let g(x) = f(t) dt, where f is the function whose graph is shown. /0 = = y 18 45 63 12 9 6 3 -3 6 3…

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Q: Q2 Suppose X₁ and X₂ has a joint pdf given by f(x₁, x2) = 6x1,0 < x1 < x2 < 1, and zero otherwise.…

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Q: etermine the equation of your model that will pass 2,4

A: We already have the equation of polynomialand

Q: = ["²F(t) Let g(x) = f(t) dt, where f is the function whose graph is shown. y 6 2 N -2 = 0 8 2 40…

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