Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = 2x3 − x2 + 7x F(x)= 2. Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = 6x5 − 4x4 − 9x2 F(x)= 3. Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = 8*squareroot(x) -3* thrid root (x) F(x)= 4. Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(?) = 3 sin(?) − 4 sec(?) tan(?) on the interval (-pi/2,pi/2) F(?) = 5. Find f. f ″(x) = −2 + 12x − 12x2, f(0) = 8, f ′(0) = 18 f(x) = 6. Find f. f ''(x) = 6 + 6x + 24x2, f(0) = 3, f (1) = 12 7. A particle is moving with the given data. Find the position of the particle, s(t). a(t) = 2t + 9, s(0) = 4, v(0) = −8 s(t) = 8. A particle is moving with the given data. Find the position of the particle, s(t). a(t) = t2 − 5t + 8, s(0) = 0, s(1) = 20 s(t) =
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = 2x3 − x2 + 7x F(x)= 2. Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = 6x5 − 4x4 − 9x2 F(x)= 3. Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = 8*squareroot(x) -3* thrid root (x) F(x)= 4. Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(?) = 3 sin(?) − 4 sec(?) tan(?) on the interval (-pi/2,pi/2) F(?) = 5. Find f. f ″(x) = −2 + 12x − 12x2, f(0) = 8, f ′(0) = 18 f(x) = 6. Find f. f ''(x) = 6 + 6x + 24x2, f(0) = 3, f (1) = 12 7. A particle is moving with the given data. Find the position of the particle, s(t). a(t) = 2t + 9, s(0) = 4, v(0) = −8 s(t) = 8. A particle is moving with the given data. Find the position of the particle, s(t). a(t) = t2 − 5t + 8, s(0) = 0, s(1) = 20 s(t) =
ChapterP: Prerequisites
SectionP.4: Factoring Polynomials
Problem 84E: The rate of change of an autocatalytic chemical reaction is kQxkx2 where Q is the amount of the...
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Concept explainers
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Question
1.
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)
f(x) = 2x3 − x2 + 7x
F(x)=
2.
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)
f(x) = 6x5 − 4x4 − 9x2
F(x)=
3.
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)
f(x) = 8*squareroot(x) -3* thrid root (x)
F(x)=
4.
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)
f(?) = 3 sin(?) − 4 sec(?) tan(?) on the interval (-pi/2,pi/2)
F(?) =
5.
Find f.
f ″(x) = −2 + 12x − 12x2, f(0) = 8, f ′(0) = 18
f(x) =
6.
Find f.
f ''(x) = 6 + 6x + 24x2, f(0) = 3, f (1) = 12
7.
A particle is moving with the given data. Find the position of the particle,
s(t).
a(t) = 2t + 9, s(0) = 4, v(0) = −8
s(t) =
8.
A particle is moving with the given data. Find the position of the particle,
s(t).
a(t) = t2 − 5t + 8, s(0) = 0, s(1) = 20
s(t) =
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