Question

Find the particular antiderivative that satisfies the following conditions:

A) p'(x)=-20/X^2 ; p(4)=3

B) p'(x)=2x^2-7x ; p(0)=3,000

C) Consider the function f(x)=3cosx−7sinx.

Let F(x) be the antiderivative of f(x) with F(0)=7

D) A particle is moving as given by the data: v(t)=4sin(t)-7cos(t) ; s(0)=0

Answer #1

1) Find the antiderivative if f′(x)=x^6−2x^−2+5 and f(1)=0
2)Find the position function if the velocity is v(t)=4sin(4t)
and s(0)=0

(a) Find the most general antiderivative of the function f(x) =
−x^ −1 + 5√ x / x 2 −=4 csc^2 x
(b) A particle is moving with the given data, where a(t) is
acceleration, v(t) is velocity and s(t) is position. Find the
position function s(t) of the particle. a(t) = 12t^ 2 − 4, v(0) =
3, s(0) = −1

Find the most general antiderivative of the function. (Check
your answer by differentiation. Use C for the constant of
the antiderivative.)
f(x) = 4x
+ 7
f(x)=
Find the most general antiderivative of the function. (Check
your answer by differentiation. Use C for the constant of
the antiderivative.)
f(x) =
9
x8
f(x)=
f '(t) = sec(t)(sec(t) + tan(t)), −− π/ 2
< t < π/ 2 , f ( π/ 4) = −3
f(t)=
Find f. f '''(x) = cos(x), f(0)...

For f(x) = 3 + 7x − 19x^2 + 2x^4, use complete Horner’s
algorithm to find
(a) the Maclaurin series (Taylor series about x = 0)
(b) the Taylor series for this function about x = 2.

For 1 and 2, give a function f that satisfies the given
conditions.
1. f ' (x) = x^5 + 1 + 2 sec x tan x with f(0) = 4
2. f '' (x) = 12x + sin x with f(0) = 3 and f ' (0) = 7

1. Consider the function f(x) = 2x^2 - 7x + 9
a) Find the second-degree Taylor series for f(x) centered at x =
0. Show all work.
b) Find the second-degree Taylor series for f(x) centered at x =
1. Write it as a power series centered around x = 1, and then
distribute all terms. What do you notice?

1. Let f(x)=−x^2+13x+4
a.Find the derivative f '(x)
b. Find f '(−3)
2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate f '(x) at x=3 rounded
to 2 decimal places.
f '(3)=
3. Let f(x)=(x^3+4x+2)(160−5x) find f ′(x).
f '(x)=
4. Find the derivative of the function f(x)=√x−5/x^4
f '(x)=
5. Find the derivative of the function f(x)=2x−5/3x−3
f '(x)=
6. Find the derivative of the function
g(x)=(x^4−5x^2+5x+4)(x^3−4x^2−1). You do not have to simplify your
answer.
g '(x)=
7. Let f(x)=(−x^2+x+3)^5
a. Find the derivative....

7. (a) Sketch a graph of a function f(x) that satisfies all of
the following conditions.
i. f(2) = 3 and f(1) = −1
ii. lim x→−4 f(x) = −∞
iii. limx→∞ f(x) = 1
iv. lim x→−∞ f(x) = −2
v. lim x→−1+ f(x) = ∞
vi. lim x→−1− f(x) = −∞
vii. f 0 (x) > 0 on (−4, −3.5) ∪ (−2.5, −1.5) ∪ (1, 2) ∪ (2,
∞)
viii. f 0 (x) < 0 on (−∞, −4)...

Evaluate the following:
1) ∫ 4? ?? and determine C if the antiderivative F(x) satisfies
F(2) = 12.
2) ∫4???=
3) ∫( ?5 + 7 ?2 + 3 ) ?? =
4) ∫ ?4( ?5 + 3 )6 ?? =
5)∫4?3 ??=?4+ 3
6) ∫ ?2 sec2(?3) ?tan(?3)??
7 ) ∫ 53 ? 13 ? ? =
8) ∫ ln8(?) ?? =?
9) ∫ 3 ln(?3) ?? =?
10) ∫ 4?3 sin3(?4) cos(?4) ?? =
11) ∫6?55?6??=
12) ∫???2(3?)??=
13)...

1.Find ff if
f′′(x)=2+cos(x),f(0)=−7,f(π/2)=7.f″(x)=2+cos(x),f(0)=−7,f(π/2)=7.
f(x)=
2.Find f if
f′(x)=2cos(x)+sec2(x),−π/2<x<π/2,f′(x)=2cos(x)+sec2(x),−π/2<x<π/2,
and f(π/3)=2.f(π/3)=2.
f(x)=
3.
Find ff if f′′(t)=2et+3sin(t),f(0)=−8,f(π)=−9.
f(t)=
4.
Find the most general antiderivative of
f(x)=6ex+9sec2(x),f(x)=6ex+9sec2(x), where −π2<x<π2.
f(x)=
5.
Find the antiderivative FF of f(x)=4−3(1+x2)−1f(x)=4−3(1+x2)−1
that satisfies F(1)=8.
f(x)=
6.
Find ff if f′(x)=4/sqrt(1−x2) and f(1/2)=−9.

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