Which of the following theorems establishes a relationship between differentiation and integration O Rolle's Theorem O Net Change Theorem O Fundamental Theorem of Calculus, Part 1 O Mean Value Theorem for Derivatives O Mean Value Theorem for Integrals O Fundamental Theorem of Calculus, Part 2

Q: Evaluate, with an exact value, the definite integral º -1/1+a dx.

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Q: 5) z = ecos(2x)

A: Given:z=ecos2x

Q: 75. F(x) : (t + 2) dt

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Q: 3. (D - 3D? + 4)y = 40cos2x + 6

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Q: Differentiation In(2) find g'(e). Let g(x): %3D -2 a) b) e? 1 c) e4 d) 4e e) e2

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Q: plicit differentiation ex sinz-zlnx + ey arccos(22) = 0 ; дz S/8

A: Given query is to find indicated partial derivative.

Q: дz дz Use implicit differentiation to find and дх ду дz дх дz ду || - || О 0 if In(xy + yz + xz) =…

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Q: tangent

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Q: sec(tan(2x)) – 4 6. dx (cos(2x))? 8. / e*-* dx T e3x-e3x

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Q: 7. A variable equilateral triangle whose plane is perpendicular to the x-axis has its two vertices…

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Q: Find the area of the surface generated by revolving about the x-axis the ellipse x = acost, y =…

A: We need to find area. NOTE - As per Bartleby's guidelines we can solve one question from multiple…

Q: Find the area enclosed by one "leaf" of the three-leaved rose: Bepaal die area wat deur 'n "blaar"…

A: Find the area enclosed by one leaf of r=4cos15θ such that -π30≤θ≤π30

Q: Determine the moment of inertia of the region bounded by the lines 3x-y=0, x-7=0, and the x-axis…

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Q: How: Approximale Approximale to Lan (1) Use the local liner approximation hear approximate tan…

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Q: ylnx – xlny = 1, find y' %3D

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Q: sin 8 cos (cos a cosec 0) do 1/2-a (1-cos a).

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Q: average rate of change fo [0,10]

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Q: Direction: Simplify the following expressions. 1. If z = 3 + 9i, determine z5.

A: De Moivre's Theorem states that if a complex number z is of the form z=rcosθ+isinθ Then zn can be…

Q: Define and explain integral and its properties briefly

A: Explanation of the answer is as follows

Q: h(t) = Vt – 4e* x+ 4x + 3 y =

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