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2. If f(x) and g(x) are continuous functions, then " g(x)] dx = | f(x)dx• g(x)dx. 3. If f(x) and g(x) are continuous functions, then Jra) + g(«)] dx = J g(x)dx + | f(x)dx. S r«»dx. 4. If f(x) and g(x) are continuous functions, then Se dx = g(x) Sf(x)dx Sg(x)dx' 5. SEdx = In|x| + C and S dx = In|x²| + C. xn+1 %3D _6. Sx" = _7. If G(x) is an antiderivative of g(x) and F(x) = G(x) – 5, then F(x) is also an antiderivative of g(x). If the integrand is positive the antiderivative is also positive. 9. The antiderivative of a function is not unique. 10. If G(x) is an antiderivative of g(x) then y = G(x) is a solution to the differential equation = g(x). 11. The differential equation = xy – y + x is separable. +C, for any real number n. n+1 dy dx dy dx _12. If a population grows exponentially, the doubling time is given by t = k is the growth constant. In 2 where k

2. If f(x) and g(x) are continuous functions, then " g(x)] dx = | f(x)dx• g(x)dx. 3. If f(x) and g(x) are continuous functions, then Jra) + g(«)] dx = J g(x)dx + | f(x)dx. S r«»dx. 4. If f(x) and g(x) are continuous functions, then Se dx = g(x) Sf(x)dx Sg(x)dx' 5. SEdx = In|x| + C and S dx = In|x²| + C. xn+1 %3D _6. Sx" = _7. If G(x) is an antiderivative of g(x) and F(x) = G(x) – 5, then F(x) is also an antiderivative of g(x). If the integrand is positive the antiderivative is also positive. 9. The antiderivative of a function is not unique. 10. If G(x) is an antiderivative of g(x) then y = G(x) is a solution to the differential equation = g(x). 11. The differential equation = xy – y + x is separable. +C, for any real number n. n+1 dy dx dy dx _12. If a population grows exponentially, the doubling time is given by t = k is the growth constant. In 2 where k

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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_2. If f(x) and g(x) are continuous functions, then Jr«) • g(*)] dx = | | g(x)dx. f (x)dx · 3. If f(x) and g(x) are continuous functions, then Jr«) + g(x)] dx = | g(x)dx + [ f«)dx. _4. If f(x) and g(x) are continuous functions, then (dx = L(x)dx Sg(x)dx' g(x _5. SEdx = In|x| + C and S dx = In|x²| + C. xn+1 + C , for any real number n. _6. Sx" _7. If G(x) is an antiderivative of g(x) and F(x) = G(x) –5, then F(x) is also an antiderivative of g(x). 8. If the integrand is positive the antiderivative is also positive. 9. The antiderivative of a function is not unique. 10. If G(x) is an antiderivative of g(x) then y = G(x) is a solution to the differential equation = g(x). n+1 dy 11. The differential equation = xy – y + x is separable. dx In 2 where _12. If a population grows exponentially, the doubling time is given by t = k is the growth constant.
Transcribed Image Text:_2. If f(x) and g(x) are continuous functions, then Jr«) • g(*)] dx = | | g(x)dx. f (x)dx · 3. If f(x) and g(x) are continuous functions, then Jr«) + g(x)] dx = | g(x)dx + [ f«)dx. _4. If f(x) and g(x) are continuous functions, then (dx = L(x)dx Sg(x)dx' g(x _5. SEdx = In|x| + C and S dx = In|x²| + C. xn+1 + C , for any real number n. _6. Sx" _7. If G(x) is an antiderivative of g(x) and F(x) = G(x) –5, then F(x) is also an antiderivative of g(x). 8. If the integrand is positive the antiderivative is also positive. 9. The antiderivative of a function is not unique. 10. If G(x) is an antiderivative of g(x) then y = G(x) is a solution to the differential equation = g(x). n+1 dy 11. The differential equation = xy – y + x is separable. dx In 2 where _12. If a population grows exponentially, the doubling time is given by t = k is the growth constant.
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