Question

An antiderivative of (90t + 540)(t^2 + 12t)^(1/2) is

A. 30(t^2 + 12t)^(3/2)

B. (t^2 + 12t)^3

C. (t^2 + 12t)^2

1. What is the derivative of A?

2. What is the derivative of B?

3. What is the derivative of C?

4. Is A or B or C the correct choice? That is, which derivative actually matches the original expression?

Answer #1

(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

What is the antiderivative of this integral?
∫(dx/(a2+x2)3/2, where a is a
constant.
a) -1/[a²√(a²+x²)]
b) -x/√(a²+x²)
c) x/[a²√(a²+x²)]
d) -1/√(a²+x²)

A particle is moving along a straight line and has acceleration
given by a(t) = 20t^3+12t^2}. Its initial velocity is v( 0 ) = 4 m
/ s and its initial displacement is s( 0 ) = 5 m. Find the position
of the particle at t = 1 seconds.

A particle is moving along a straight line and has acceleration
given by a(t) = 20t^3+12t^2}. Its initial velocity is: v(0) = 4 m/
and its initial displacement is s(0) = 5 ms. Find the position of
the particle at t = 1 seconds.
10 m
5 m
11 m
4 m
2m

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

Find a power series representation for the function:
?(?)=?^(2)arctan(?3)
?(?)=(?/(2−?))^3
Express the antiderivative as a power series;
∫?/(1+t^(3) ??
∫arctan(?)/(?)??

Find the most general antiderivative of the function. (Check
your answer by differentiation. Use C for the constant of
the antiderivative.)
1.)f(x) = 5/x^4
2.)f(t) = 2+t+t^2 / sqrt (t)
3.)f(x) = 7sqrt(x^2) + xsqrt(x)

1. Let T = {(1, 2), (1, 3), (2, 5), (3, 6), (4, 7)}. T : X ->
Y. X = {1, 2, 3, 4}, Y = {1, 2, 3, 4, 5, 6, 7}
a) Explain why T is or is not a function.
b) What is the domain of T?
c) What is the range of T?
d) Explain why T is or is not one-to one?

At what point do the curves r1 =〈 t
, 1 − t , 3 + t2 〉 and r2 =
〈 3 − s , s − 2 , s2 〉 intersect? Find the angle of
intersection.
Determine whether the lines L1 :
r1 = 〈 5 − 12t , 3 + 9t ,1 − 3t 〉 and
L2 : r2 = 〈 3 + 8s , −6s , 7
+ 2s 〉are parallel, skew, or intersecting. Explain. If...

Find the derivative of the function.
h(t) = (t + 4)2/3(3t2 − 2)3

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