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These are the notes of Exam of Calculus which includes Traditional Problems, Symmetric Matrix, Property, Conditions, Constants, Matrix, Positive, Anti Symmetric etc. Key important points are: Policies, Receiving Unauthorized, Honor Code Violation, Computer, Arc Length, Graph, Integral, Constant Acceleration, Calculate, Information
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INSTRUCTIONS Please enter your NAME, ID NUMBER, FORM designation letter,
and CRN on your op scan sheet. The CRN should be written in the upper right-hand box
labeled “Course.” Do not include the course number. In the box labeled “Form,” write the
appropriate form letter as shown above. Darken the appropriate circles below your ID
number and Form designation. Use a #2 pencil.
Mark your answers to the test questions in rows 1-15 of the op scan sheet. You have one
hour to complete this part of the final exam. Your score on this part will be the number of
correct answers. Turn in the op scan sheet with your answers and the question sheets,
including this cover page, at the end of this part of the final exam. Any additional parts of
the exam will begin after all students have completed this common part.
Exam policies You may not use a book, notes, formula sheet, calculator, or computer.
Giving or receiving unauthorized aid is an Honor Code Violation.
1. Evaluate
2 ln x 2ln x 7 dx x
(a)
3 2
2
ln x ln x 7x 3 C x
2
3 ln x (^2) ln x 7x C 3
(c)
3 ln x (^2) ln x 7 ln x C 3
2ln x C x
2. The arc length of the graph of y = sin x, 0 < x < π, is given by the integral
(a) 0
1 sin x dx
π
(b) 0
1 cos x dx
π
(c)
2
0
1 sin x dx
π
(d)
2
0
1 cos x dx
π
3. A particle moves along the x-axis with a constant acceleration of a = 2 units per
second per second. At time t = 0 it is at the point x = 5 and has a velocity v(0) = 4 units
per second. What is its velocity, in units per second, when it reaches the point x = 17?
(a) 8 (b) 17 (c) 4
(d) Impossible to calculate from this information
4. The region bounded by the graphs of y = x
2 and y = 4 − x
2 is revolved about the x-
axis. The integral for the volume of the solid of revolution is
(^2 ) 2 4
0
π ^4 − x −x dx
2 2 2
0
π ^4 − x −x dx
(^2 ) 2 4
2
4 x x dx −
π − −
2 2 2
2
4 x x dx −
π ^ − −
5. The region bounded by the graphs of y = x
2 and y = 4 − x
2 is revolved about the line
x = − 4. The integral for the volume of the solid of revolution is
2 2
0
2 π x 4 −2x dx
2 2
2
2 x 4 4 2x dx −
π − −
2 2
2
2 x 4 4 2x dx −
π + −
(d) None of the above
6. The Fundamental Theorem of Calculus states that 2
1 3
x
d t 1 dt dx
equals
(a) 3 x + 1 (b) 3 − x + 1
(c)
6 2x x + 1 (d)
6 − 2x x + 1
7. It took 2 pounds of force to stretch a spring one inch beyond its natural length of 20
inches. How much work (in inch-pounds) is needed to stretch it one inch further?
(a)
2
1
2x dx
(b)
22
21
2x dx
(c)
2
1
2x dx
(d)
22
21
2x dx
12. (^) 2
5x 4 dx x x 2
=
(a)
2 1 x^1 5ln x x 2 4 tan C x 2
(b) 3ln x − 1 + 2ln x + 2 +C
(c)
2 5ln x + x − 2 + C (d) 3ln x − 1 − 2ln x + 2 +C
13. 2
dx
=
2 2 2x x 6x 10 C
−
2 ln (x + 6x + 10) +C
(c) tan
ln x 2 ln x 5 C 2 2
14.
2 x x e dx
=
(a)
2 x x x x e + 2xe + 2e + C (b)
2 x x x x e − 2xe + 2e +C
(c) 2 x x x x e + xe + e + C (d) 2 x x x x e − xe + e +C
15.
5x
x
lim 1 →∞ x
=
(a) 15 (b) e 15 (c) 5/3 (d) e 5/
16. The Simpson’s Rule approximation for
3
1
ln x dx
with 4 subdivisions is
(a)
ln1 4ln 2ln 2 4ln ln 3 6 2 2
(b)
ln1 4ln 2ln 2 4ln ln 3 6 2 2
(c)
ln1 2ln 2ln 2 2ln ln 3 2 2 2
(d)
ln1 2ln 2ln 2 2ln ln 3 2 2 2