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Calculus

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Q: Use partial fractions, completing the square, and/or integration tables to find the following defini...

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Q: Find all the continuous positive functions f(x), for 0 ≤ x ≤ 1, such that where α is a given real nu...

A: Given: The real number is α The integral functions are,

Q: Find the derivative of the function y = tanh−1(sin 2x)

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Q: Circulation and flux Find the circulation and the outward flux of the following vector fields for th...

A: Given: (i). F = ⟨x - y, x⟩ (ii). r(t) = ⟨2 cost, 2 sint⟩ , for 0 ≤ t ≤ 2π To Find: Circulation and o...

Q: Divide numerator and denominator by the highest power of x in thedenominator and proceed from there....

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Q: Question in picture

A: Given data: The given integral is: . The expression for the Green’s theorem is, Compare it wi...

Q: Find the derivative of the function y = tanh−1√x

A: To find the derivative of the given function.

Q: express the given complex-valued function in the form u(x) +iv(x) for appropriate real-valued functi...

A: Given:

Q: Consider the vector field F = ⟨ 1 , y ⟩ .Compute the path integral of this field along the path: st...

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