Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) r(?) = sec(?) tan(?) − 8e? R(?) =

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Q: Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then…

A: A detailed solution is given below.

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A: We have to find the directional derivative.

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A: Given that , The rate of change of the temperature of the water is dTdt=-10e-0.2t

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Q: Can you please write it out I can't read it typed.

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A: The objective of the question is evaluate the area by help of midpoint rule.

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A: We have to find the value of f'(-1).

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A: given : Suppose d(10!*x) = 2700, here x is another integer and  gcd(10!, x) =1.

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Q: Evaluate the definite integral (a) ľ² _l+ x +24 dx, (b) [¹² (x² + 3) (2x + 1)dx, (c) [¹ x²e²¹dx -1…

A: ∫-11 xdx1+x2+x4

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A: The given function fx,y=2x3-6x+6xy2

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A: The objective is to find the solution.

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A: We need to find derivative.

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A: We need to determine equation of parabola.

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A: We will solve to get required result.

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Q: specfically though, tell me what i'd put in EACH specfiic box.

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A: We can find the limit as below.

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A: Topic = Vector

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A: We can answer the question as below by filling up the blanks.