Rehman (aar638) HW04 sachse (56620) This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. 001 10.0 points Thus we need to nd
2 1
1
f (x)dx = F (2) F (1) .
Now
2 2
The gr
Version 038 L FINAL EXAM Neitzke (56585) This print-out should have 25 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. 001 10.0 points 1. I = 52
1
1
respectively. Use these to nd the value of t
jones (bwj276) HW02 neitzke (55460)
1
4
This print-out should have 13 questions.
Multiple-choice questions may continue on
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before answering.
3
2
2
1
001
10.0 points
If g (x) is continuous on [a,b] and m is a
constant
pham (pp8458) HW07 neitzke (55460)
This print-out should have 23 questions.
Multiple-choice questions may continue on
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before answering.
001
(ii) f has a vertical asymptote at one or
more of x = a, x = b or x = c for
elghonimi (sie94) HW01 hong (52950)
4
4. f (x) = sin(x) cos(sin(x)
1. f (x) = ex cos(ex ) correct
5. f (x) = sin(x) cos(sin(x)
2. f (x) = ex sin(ex )
6. f (x) = cos(x) sin(cos(x)
3. f (x) = ex cos(ex )
Explanation:
Using the Chain Rule we see that
f (x) =
elghonimi (sie94) HW01 hong (52950)
Since the limit has the form 0/0, it is indeterminate and LHospitals Rule can be applied:
lim
x0
f (x)
f (x)
= lim
x 0 g (x)
g(x)
and
6
g(x) = 2 sin2 x .
Then f, g are twice-dierentiable functions
such that
lim f (x) =
elghonimi (sie94) HW01 hong (52950)
Consequently,
5
2. f (x) = e12/x
f () = 6 cot 6 .
3. f (x) = 11x12
011
10.0 points
Determine the value of f (1) when
f (x) = 3 ln (x + 1) .
1. f (1) =
3
8
2. f (1) =
3. f (1) =
4 4 ln(x3 )
e
x2
5. f (x) = 12x11 correct
elghonimi (sie94) HW01 hong (52950)
when a > 0, evaluating the limit directly
gives
1. f (x) =
ex 5ex
5ex + 4ex
2. f (x) =
lim
x
=
,
which doesnt make any sense. (And we cant
just cancel the s because innities dont
work like that.) So we try to get rid o
elghonimi (sie94) HW01 hong (52950)
This print-out should have 20 questions.
Multiple-choice questions may continue on
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before answering.
001
002
1
10.0 points
Determine
lim
x1
x 0 x2 (x +
10.0 points
Determine if
6)
elghonimi (sie94) HW01 hong (52950)
Determine if
lim
x2
1
1
ln(x 1) x 2
on (1, ), so we can use LHospitals Rule yet
again:
lim
x2
exists, and if it does, nd its value.
f (x)
f (x)
= lim
x 2 g (x)
g(x)
with
1. limit =
f (x) =
2. limit = 1
3. limit =
7
1
elghonimi (sie94) HW02 hong (52950)
2.
Explanation:
Since
1
0,
3
3. (3, ) correct
1
,
3
4.
0,
5.
7
(3, )
1
,3
3
1
= sec2 ,
2
cos
d
tan = sec2 ,
d
we see that
/6
I =
0
(3 sec2 2 cos ) d
6. (0, 3)
Explanation:
The graph of F will be concave down when
F (x)
elghonimi (sie94) HW02 hong (52950)
6. F (x) = 6x 1 +
4
By the Fundamental Theorem of Calculus
and the Chain Rule,
x2
Explanation:
By the Fundamental Theorem of Calculus
and the Chain Rule,
g(x)
d
dx
a
When
g(x)
d
dx
f (t) dt
= f (g(x)g (x) .
f (t) dt
= f
elghonimi (sie94) HW02 hong (52950)
5
Taking
1
F (y) = y + 3y y 3 ,
3
2
012
Evaluate the denite integral
/2
we thus see that
I =
8
I = 2 + 12 .
3
0
(cos x 3 sin x) dx .
1. I = 5
Consequently,
34
.
3
I =
011
10.0 points
Evaluate the integral
4
x 3 x dx .
I
elghonimi (sie94) HW02 hong (52950)
If f is a continuous function such that
x
8x
f (t) dt = 2
,
x +5
0
nd the value of f (1).
3
3. g (x) = 3x2 tan x
4. g (x) = 6x sec x tan x
5. g (x) = 6x sec2 x
1. f (1) =
17
18
6. g (x) = 3x2 tan x correct
2. f (1) =
8
elghonimi (sie94) HW02 hong (52950)
By the Fundamental theorem of calculus,
determine the value of F (1).
2
F (x) = 3 e10 sin x .
1. F (1) = 2
At x = /4, therefore,
2. F (1) = 4
3. F (1) = 24
dF
dx 4
4. F (1) = 16
since
5. F (1) = 8 correct
sin
Explanati
elghonimi (sie94) HW01 hong (52950)
020
10.0 points
Use properties of integrals to determine the
value of
0
I =
f (x) dx
4
when
6
6
f (x) dx = 8,
0
f (x) dx = 3 .
4
1. I = 11
2. I = 5
3. I = 5 correct
4. I = 8
5. I = 8
6. I = 11
Explanation:
Since
a
b
b
f
elghonimi (sie94) HW01 hong (52950)
is the graph of a function f , use rectangles to
estimate the denite integral
10
I =
019
10.0 points
For which integral, I, is the expression
|f (x)| dx
0
9
by subdividing [0, 10] into 10 equal subintervals and taking r
elghonimi (sie94) HW02 hong (52950)
This print-out should have 18 questions.
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before answering.
001
10.0 points
The graph of f is shown in the gure
6
6
5
4
4
3
2
2
1
0
-1
-2
2
elghonimi (sie94) HW01 hong (52950)
8
we rst take logs and then evaluate
4. III only
1
.
lim ln (1 3x) 5x
x 0+
5. II only correct
But
ln(1 3x)
.
5x
1
ln (1 3x) 5x
=
By LHospitals Rule, therefore,
1
Explanation:
Property II is a special case of the lineari
elghonimi (sie94) HW06 hong (52950)
1. I =
2
9
3. I =
2. I =
2
4
4. I =
2
3. I =
8
2
3
4
4
5. I =
4. I =
3
3
4
3
3
6. I =
2
72
017
2
5. I =
18
10.0 points
Determine the integral
015
3 2x
dx .
x2 1
I =
10.0 points
Determine the integral
1
dx .
2 x2 1
x
I =
elghonimi (sie94) HW06 hong (52950)
4. I =
5. I =
1
( 2)
4
019
10.0 points
Evaluate the integral
/2
I =
(3 sin() + 2 sin3 () d .
0
1. I =
13
3
2. I =
11
3
3. I = 1
4. I =
5
3
5. I =
7
3
6. I = 5
020
10.0 points
Determine the integral
5
dx .
x x2 + 9
I =
3
elghonimi (sie94) HW03 hong (52950)
This print-out should have 22 questions.
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before answering.
001
10.0 points
Determine the integral
5 2x
dx .
x
I =
1. I = 5 x1/2 +
4 3/2
x
elghonimi (sie94) HW03 hong (52950)
If f is a continuous function such that
3. I =
8
f (x) dx = 8 ,
0
determine the value of the integral
4
I =
3f (2x) dx .
4
1 3
sin x + C
3
1
4. I = cos3 x + C
3
5. I =
1 2
sin x + C
2
0
6. I = cos x + C
1. I = 11
018
2.
elghonimi (sie94) HW03 hong (52950)
2. Miras weight at age 2
5. 5.0 miles south of Austin
3. increase in Miras weight from age 2 to 8
4. Miras weight at age 8
5. decrease in Miras weight from age 2 to 8
006
008
f (t) =
176
(t + 5)2
barrels per month (in m
elghonimi (sie94) HW03 hong (52950)
5. I =
3
1
+C
2 sin
2
6. I =
6. I =
1
3
+C
2 sin
2
020
5
3
5+1
4
022
10.0 points
Evaluate the integral
10.0 points
e4
I =
e
Evaluate the integral
1
4 e2x
I =
2
+ln x
dx .
0
2. I = 8
1. I = e2 1
3. I = 9
e2 1
e2
2. I
elghonimi (sie94) HW04 hong (52950)
This print-out should have 11 questions.
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001
1
3. area = 18 sq.units
4. area =
32
sq.units
3
10.0 points
Find the area o
elghonimi (sie94) HW04 hong (52950)
2
125
sq. units
6
5. Area =
005
2
4.
2
4
6
2
2
10.0 points
4
6
2
4
For which one of the following shaded regions is its area represented by the integral
4
0
1
(x + 1) x
2
dx ?
6
6
5.
4
2
2
1.
2
2
4
6
2
2
2
4
006
Express