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Which of the following statements are TRUE? Select all that apply. If F(x) is an antiderivative of f (x) and G (x) is an antiderivative of g(x), then: f(f(x)+g(x)) dx = F(x) + G (x) + C An antiderivative of a linear function is a linear function. The most general antiderivative of f (x) = 2ex + 16x3 +3 is given by F(x) = 2ex + 4x4 + 3x + C. 6x2 Of 2-3 dx = 2. -3x 2x3 + C An antiderivative of f (x) = 3 sin x is F (x) = −3 cos x + 2π ☐ An antiderivative of ƒ (x) = 6√√x+3 is F(x) = 4(x+3) 3 2 If F(x) is an antiderivative of f (x) and G (x) is an antiderivative of g (x) " then: ƒ ƒ (x) · g(x) dx = F(x) · G(x) + C If F(x) is an antiderivative of f (x), then: fxf(x) dx=xF(x) +C If F (x) is an antiderivative of f (x) and G (x) = F(x) +7, then G (x) is also an antiderivative of f (x).

Which of the following statements are TRUE? Select all that apply. If F(x) is an antiderivative of f (x) and G (x) is an antiderivative of g(x), then: f(f(x)+g(x)) dx = F(x) + G (x) + C An antiderivative of a linear function is a linear function. The most general antiderivative of f (x) = 2ex + 16x3 +3 is given by F(x) = 2ex + 4x4 + 3x + C. 6x2 Of 2-3 dx = 2. -3x 2x3 + C An antiderivative of f (x) = 3 sin x is F (x) = −3 cos x + 2π ☐ An antiderivative of ƒ (x) = 6√√x+3 is F(x) = 4(x+3) 3 2 If F(x) is an antiderivative of f (x) and G (x) is an antiderivative of g (x) " then: ƒ ƒ (x) · g(x) dx = F(x) · G(x) + C If F(x) is an antiderivative of f (x), then: fxf(x) dx=xF(x) +C If F (x) is an antiderivative of f (x) and G (x) = F(x) +7, then G (x) is also an antiderivative of f (x).

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 5CR: Determine whether each of the following statements is true or false, and explain why. The chain rule...
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Which of the following statements are TRUE? Select all that apply. If F(x) is an antiderivative of f (x) and G (x) is an antiderivative of g(x), then: § (ƒ (x) + g(x)) dx = F(x) + G(x) + C An antiderivative of a linear function is a linear function. The most general antiderivative of ƒ (x) = 2e² + 16x³ +3 is given by F(x) = 2ex +4x² +3x+C . ○ √ 22-3³ dx = x²-3 +C Of 6x2 2x3 An antiderivative of ƒ (x) = 3 sin x is F (x) = −3 cos x + 2π 3 An antiderivative of ƒ (x) = 6√√x+3 is F(x) = 4(x+3)ź ☐ If F(x) is an antiderivative of ƒ (x) and G (x) is an antiderivative of g(x) then: ƒ ƒ (x) · g(x) dx = F(x) · G (x) + C ☐ If F(x) is an antiderivative of f (x), then: fxf(x) dx = xF(x) +C If F(x) is an antiderivative of f (x) and G (x) = F(x) + 7, then G (x) is also an antiderivative of ƒ (x).
Transcribed Image Text:Which of the following statements are TRUE? Select all that apply. If F(x) is an antiderivative of f (x) and G (x) is an antiderivative of g(x), then: § (ƒ (x) + g(x)) dx = F(x) + G(x) + C An antiderivative of a linear function is a linear function. The most general antiderivative of ƒ (x) = 2e² + 16x³ +3 is given by F(x) = 2ex +4x² +3x+C . ○ √ 22-3³ dx = x²-3 +C Of 6x2 2x3 An antiderivative of ƒ (x) = 3 sin x is F (x) = −3 cos x + 2π 3 An antiderivative of ƒ (x) = 6√√x+3 is F(x) = 4(x+3)ź ☐ If F(x) is an antiderivative of ƒ (x) and G (x) is an antiderivative of g(x) then: ƒ ƒ (x) · g(x) dx = F(x) · G (x) + C ☐ If F(x) is an antiderivative of f (x), then: fxf(x) dx = xF(x) +C If F(x) is an antiderivative of f (x) and G (x) = F(x) + 7, then G (x) is also an antiderivative of ƒ (x).
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