Transcribed Text
1.
Evaluate the integral
11/4dx.
The value of the integral
11/4dxis
(Simplify your answer.)
ID:5.4.8
2.
Solve the following initial value problem.
y
3 sint +2 cost with y""(0)=9,y"(0)=2,y((0)= 3,y(0)=(
Sketch the graph of continuous function y  g(x) that satisfics the conditions given below
(a) 02 1
.
as x>2
(b) g(2)5,g for x2. g'(x)> >>> forx>2 and
(a) Choose the correct graph below
Or
OB
OC
OD
(b) Choose the correct graph below
OA
OB.
Oc
OD
U3
A
baseball diamond is a square 90 on side player runs
from base second rate of 16 ft/sec
a.
thwat rate the player' distance from third base changing
when the player 30f from first base?
b.At what rates are angles 8, and 0, (see the figure) changing
at that time?
The player slides into second base the rate of 18 1/sec. At
what rates are angles changing player
touches base?
a. The rate ft/sec.
(Type exact answer, using radicals needed.)
b. When the player 30' from first base, what are the rates of change of the angles @ and 0,2
rad/sec
(Simplify your answers Use comma to separate s needed.)
c. As the player slides into second base at a rate of 18 ft sec. what are the rates of change the
angles rad/scc
(Simplify your answers. Use comma to separate answers s needed.)
ID: 3.8.43
Find the limitof {xx=
asx approaches andas approaches 00.
9
lim f(x)=
(Type simplified fraction.)
lim f(x)=
(Type a simplified fraction.
Find the absolute maximum and minimum values of the function on the given interval. Then graph
the function Identify the points on the graph where the absolute extrema occur.
((x)23, 025x52
The absolute maximum
The absolute minimum i
at x
=
Choose the correct graph of the function.
OA
OB.
Oc
x
1014
5042
Abs Max
4
Abs Max
x
Abs Max
20
20
Abs Min x
50
10%
2
Abs Min
Min
ID: 4.1.25
7.
What values of and b maximize the value o
(Hint Where the integrand positive?)
and b maximize the given integral
(Simplify your answer. Type whole number.)
8.
TX
Find the tangent the curvey
cot
3.
12
The
tangent
to the
curvey
6 cot
12
it Typean exact answer, T'ppe anexpression using xas the lei
variable.)
D
9
A right triangle whose hypotenuse V13 m long revolved about one of its legsto generate
right circular cone. Find the radius, height, and volume the concof greatest volume that can be
made way.
The height the cone i
m
(Round to thenearesttenth.)
The radius of the cone
m.
(Round to the nearest tenth.)
The volume of the code is m³
(Round to neares tenth.)
D
Find the first and second derivatives of the function.
(x+3)(x23x+9)
x³
dy
The first derivative of the function
dx
d3
The second derivative of the function i
dx
cos (5x)
First use L'Hopital's Rule oveluate
lim
Then determine the limit using limit laws
25x²
and commonly known limits.
1cos (5x)
Jim
L'Hopital's Rule is
25x
(Type an integer simplified fraction.)
Choose the limit equivalent to the given limit that can be evaluated using limit laws and commonly
known limits
O.A.
sin(5x)
lim (5x)2
cos
(5x)
25x
(5x)
sin(5x)
(5x)

lim
5x
5x
(1+cos(5x))
OD.
sin(5x)
(5x)2 (1) cos(5x))
The limit by substitution is
7.
(Type integer or : simplified fraction.)
12
For the function given below. find a formula for the Riemann sum obtained by dividing the interval
0, 1 into n equal subintervals and using the righthand endpoint for each Ck Then take limit of
this sum as n  co to calculate the area under the curve over (0, 11.
f(x) x+5x²
Which of the following expressions gives the formula for the Riemann sum for the given function
over the interval 11?
OA £(A)
OB
Oc
OD
k1
Simplify the sigma notation to find the sum in terms of only Choose the correct answer below
18n
13 18n5
OA
OB.
13 18n+5
OC.
O.D.
13 18n + 5
6n
What
(Simplify Type an integer fraction.)
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