I. Read carefully the statements below. Write TRUE if the statement is always correct, otherwise, FALSE. Use the space provided before each item. (1 point each) 1. There is no function f(x) such that f f(x) = f(x) + C. If f(x) and g(x) are continuous functions, then 2. [[f(x) · g(x)] dx = f f (x)dx · f g(x)dx. 3. If f(x) and g(x) are continuous functions, then [[f(x) + g(x)] dx = f g(x)dx + [ f(x)dx. __4. If ƒ(x) and g(x) are continuous functions, then ff(x) dx = ff(x) dx lg(x)dx _5. S=dx = In[x] + C and dx = In|x²| + C. xn+1 6. Sxn = + C, for any real number n. n+1 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 dy equation = g(x). dx 11. The differential equation =xy-y + x is separable. dx 12. If a population grows exponentially, the doubling time is given by t = n2, where k k is the growth constant.
I. Read carefully the statements below. Write TRUE if the statement is always correct, otherwise, FALSE. Use the space provided before each item. (1 point each) 1. There is no function f(x) such that f f(x) = f(x) + C. If f(x) and g(x) are continuous functions, then 2. [[f(x) · g(x)] dx = f f (x)dx · f g(x)dx. 3. If f(x) and g(x) are continuous functions, then [[f(x) + g(x)] dx = f g(x)dx + [ f(x)dx. __4. If ƒ(x) and g(x) are continuous functions, then ff(x) dx = ff(x) dx lg(x)dx _5. S=dx = In[x] + C and dx = In|x²| + C. xn+1 6. Sxn = + C, for any real number n. n+1 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 dy equation = g(x). dx 11. The differential equation =xy-y + x is separable. dx 12. If a population grows exponentially, the doubling time is given by t = n2, where k k is the growth constant.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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I need the answers of #8-#12.
![I. Read carefully the statements below. Write TRUE if the statement is always correct,
otherwise, FALSE. Use the space provided before each item. (1 point each)
1.
There is no function f(x) such that f f(x) = f(x) + C.
If f(x) and g(x) are continuous functions, then
2.
[[f(x) · g(x)] dx = f f (x)dx · f g(x)dx.
3. If f(x) and g(x) are continuous functions, then
[[f(x) + g(x)] dx = f g(x)dx + [ f(x)dx.
__4.
If ƒ(x) and g(x) are continuous functions, then ff(x) dx =
ff(x) dx
lg(x)dx
_5. S=dx = In[x] + C and dx = In|x²| + C.
xn+1
6. Sxn
= + C, for any real number n.
n+1
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
dy
equation = g(x).
dx
11. The differential equation =xy-y + x is separable.
dx
12. If a population grows exponentially, the doubling time is given by t = n2, where
k
k is the growth constant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b862d56-c726-471c-a8ce-b1e756c0abe0%2F2b087949-0859-4713-8fda-fc283ad8e8bb%2Fmgipcx3_processed.png&w=3840&q=75)
Transcribed Image Text:I. Read carefully the statements below. Write TRUE if the statement is always correct,
otherwise, FALSE. Use the space provided before each item. (1 point each)
1.
There is no function f(x) such that f f(x) = f(x) + C.
If f(x) and g(x) are continuous functions, then
2.
[[f(x) · g(x)] dx = f f (x)dx · f g(x)dx.
3. If f(x) and g(x) are continuous functions, then
[[f(x) + g(x)] dx = f g(x)dx + [ f(x)dx.
__4.
If ƒ(x) and g(x) are continuous functions, then ff(x) dx =
ff(x) dx
lg(x)dx
_5. S=dx = In[x] + C and dx = In|x²| + C.
xn+1
6. Sxn
= + C, for any real number n.
n+1
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
dy
equation = g(x).
dx
11. The differential equation =xy-y + x is separable.
dx
12. If a population grows exponentially, the doubling time is given by t = n2, where
k
k is the growth constant.
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