Question

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

Answer #2

answered by: anonymous

(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 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

1- Find f.
f '''(x) = cos(x), f(0) =
8, f '(0) = 6, f
''(0) = 5
2- The graph of a function f is shown. Which graph is
an antiderivative of f?
a,b,c
3- A stone was dropped off a cliff and hit the ground
with a speed of 112 ft/s. What is the height of the cliff? (Use 32
ft/s2 for the acceleration due to gravity.)
ft
4- A company estimates that the marginal cost (in dollars per
item) of...

Find the antiderivative
f(x) = 3x^2 + 4x + 5
f(x) = 3 cos x
f(x) = e^2x + 4x^3
f(x) = sec^2 x

A moving particle starts at an initial position
r(0) = <1, 0, 0> with initial velocity
v(0) = i - j +
k. Its acceleration is a(t) = 4t
i + 4t j +
k.
Find its velocity, v(t), and position,
r(t), at time t.

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)...

Find the domain of the function f(x) = 2x-6 over (2x-6)square
root x-1

1) find the
absolute extrema of function f(x) = 2 sin x + cos 2x on the
interval [0, 2pi]
2)
is f(x) = tanx
concave up or concave down at x = phi / 6

Find the velocity and position vectors of a particle that has
the given acceleration and the given initial velocity and
position.
a(t) = 4t, et, e−t v(0) =
0,0,−5 r(0) = 0,1, 4

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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