MATH 147
EXAM I
VERSION B
N~E
---------------------------------
SECTION # _ _ _ __
SEAT # _____ _
Clearly mark answers to the multiple choice problems on your paper and your scantron.
In order to obtain full credit for partial credit problems, all work must be shown. Credit will not
be given for an answer not supported by work.
"An Aggie does not lie, cheat or steal or tolerate those who do."
Clearly mark answers to the multiple choice problems on your paper and your scantron.
1. [5 pts] Which of the following functions corresponds with the scmilog graph below.
(a) y
= 8x-13
(b) y
4o(sr
(d) y =
101._____._
0
0.2
= 4logx
__.__
____.__
_.__
0.4
0.6
0.8
(e) none of these
_.___....___..___._____._
1.2
1.4
1.6
1.8
__.
2
2. [5 pts] Use a logarithmic transformation to find a linear relationship between appropriate transformations of
x and y if y
= 2 · 7 4x •
(a) logy
= 14 + log(4x)
(b) logy
= (4log7)x + log2
(c) logy = 2&x + log2
(d) logy
= 21og7 +log (4x)
(e) none of these
3. [5 pts] Find the limit, if it exists for lim x2
x-+2
+ 5x 2- X
14
(a) -9
(b) 9
(c)
oo (dne)
(d) - oo (dne)
(e) none of these
4. [5 pts] Find the limit, ifitexists for lim sin2xsin5x
x--.o
(a) dne
(b)
10
3
(c)
1
3
(d)
0
(e) none of these
3x2
5. [5 pts] Find the limit, if it exists for
lim
x-.-.c.o
2x4 + 2x + 3
x(l- x2)
(a) - 1
(b)
1
(c)
2
(d) - oo (dne)
(e) none ofthese
6. [5 pts] Find the limit, if it exists for
lim
X-40 -
(a) - I
(b) 0
(c) oo (dne)
(d) - oo (dne)
(e) none of these
1
..!.X - -lxl'
.
7. [5 pts] Compute /'(0) where f(x)
= ·{sinx,
x,
x
~0
x>O
(a) 1
(b) -1
(c) dne
(d) 0
(e) none of these
8. [5 pts] Find a value c so that the following function is continuous for all values ofx:
2
f(x) = { x + 1, x
X-· C,
(a) 0
(b) I
(c) - 1
(d) 2
(e) none of these
~1
X>
1
X
9. [5 pts] Find all points at which - - - is continuous.
In (1- x)
(a) (-oo,l)u(l,oo)
(b) (-oo,O) u (0, 1)
(c) (-oo, l)
(d) (-oo,O) u (0, 1]
(e) none of these
10. [5pts.] Solvefor x given
(a) - 1,11
(b)
11
(c) - 1,2
(d)
2
(c) none of these
log(x2 -l)-log(x+l)=l.
x3
11. [6 pts] Use the limit definition of the derivative to find /'(0) for f(x) =
-lxl'
x:;t;O
0' x=O
12. [5 pts] A radioactive isotope has a half-life of 1200 years. What is the decay rate?
13. [10 pts.] Given the doublelog plot below, find a functional relationship between x andy.
10
10CL.,__ _...._~.__......._....._..........__.......~----'---~---'---'---'-...._......o....J
10°
10 1
10:
14. Compute each ofthe following limits.
(a) [6 pts.]
lim
~x
2
+I -
x-tl
(b) [6 pts.]
..[X+T
x-1
lim secx - I
x-tO
XSeCX
15. [4 pts.] The function f(x) =
I-_!_
X
is a one-to-one function on its domain. Find f -•.
\ n~fN rlv;-'" V
*N> m...t 'fY\
16. [8 pts.] Use the biseetion method to approximate a root of x 4 + x 3 + x -1 = 0 with maximum error less
o1u.!
than~.1.
17. [5 pts.] Determine whether the function f(x) =
{xsm(H
0,
Explain why or why not.
is continuous at x
x=O
= 0.