B. condition to determine the exact value of any constant you introduce. Use separation of variables to solve the following initial value problem. Be sure to use the initial dy 1 2t /1- y? with y(0) dt for -1 < y < 1,

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A: Given the equation y=x3-3x2+3. The objective is to determine all critical points and classify using…

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A: The given function is quadratic and substituting with the provided values , we get…

Q: 324y/" – 180y' + 25y = 0, %3D y(0) = 8, y'(0) = 5. y =

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A: Given: The equation of curve fx=x3+3x2-2x-8 and the x-coordinate of point  is x=1, To find: The…

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Q: B. Find the derivative of the function. 1. y = 3 2. f(x) = x + 1 3. f(t) = -2t + 3t- 6 4. f(x) = x?…

A: Since you have posted question with multiple subparts, here is the solution for the first three…

Q: 3. y = V(p³ + 5) (p² – 6) %3D -

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Q: Find the derivative of f(x) = (v5x – 2)°. Final answer must have no parentheses.

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Q: 2x Find F'(x) given F(x) = S t2dt. -2x

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Q: Find y as a function of t if 25y"- 70y' + 53y = 0, and y(5) = 8, y'(5) = 1. %3D y = %3D

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Q: Assume and y are functions of a third variable t. If xy = 30 and 0-6 0-30/5/20 O-12 0- 10, find dt…

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Q: 2x2 at the point where x = 1. 6. Find the equation of the tangent line to the graph of f(x) = x +1

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Q: y = √sin(7x + In(5x))

A: We know that the derivative of x^n=nx^(n-1) So derivative of sqrtx=1/(2sqrtx)

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A: Proceed as shown...

Q: Trace the curve y? = (x - 1)(2x + 3)(3x – 1). %3D

A: Trace the curve y2=(x-1)(2x+3)(3x-1)

Q: F. Find the derivative of each quotient 4x+9 b. h(x) = 3r2-1 3x a. h(x): c. h(x) = - %3D 1-10…

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