Spring 2013
Math 121
Review Exam 3
1. Dierentiate the following:
a. f (x) = 6x3 +
2
e2x (x2 9),
x2
c. h(x) = 2x6 ln(x) ex
e. p(w) =
2 +4x
+
b. g(x) = 2e3x + ln(x2 ) 5,
e4x
2,
1
2 ln(w) + w
w2/5 + 3 ew ,
38
w
w
g. r (x) = e2x (x3 5x + 7)4
x2
7x
,
+ 2x +
Fall 2002
Complete Solutions 1 x 1 x
Derivative of ex and ln(x)
3. Rewrite the function f (x) = 5 ln 2, then f (x) = 5
e2x + 2 = 5 ln(x1 ) e2x + 2 = 5 ln(x) e2x + (2)e2x + 0 = 5 + 2e2x . x
4. Rewrite the function 1 3 1 1 f (x) = 5x + 4 ln = 3e5x + 4 ln(x
Spring 2001
Complete Solutions
Discrete Malthusian Growth
1. a. Since P0 = 50, 000 and r = 0.08, the general solution to this Discrete Malthusian growth model is given by Pn = 50, 000(1.08)n . It follows that P1 = 50, 000(1.08) = 54, 000 P2 = 50, 000(1.08
Spring 2001
Complete Solutions
Linear
In Problems 1-6, write the equations in the form y = mx + b, then m is the slope and b is the y-intercept. 3. From x y = 2, we have y = x 2, so m = 1 and b = 2
2 5. From 5y + 2x = 9, we have 5y = 2x 9 or y = 5 x 9 , s
1
Running head: THERE ARE NO CHILDREN HERE REFLECTION
There Are No Children Here Reflection
Anita Deodat
San Diego State University
2
THERE ARE NO CHILDREN HERE REFLECTION
There Are No Children Here Reflection
The struggles that African Americans have exp
1
Heung-Joon Park in 2001 developed an analytical method that focused on
delamination bearing strength of bolted joints using the Ye-delamination failure criterion in
conjunction with an accurate three-dimensional contact stress analysis.
3D analyses.
Cou
Maria Olague
CFD 590
Pamela Gardner
March 10, 2016
Journal Seven
My visit today in the SEEK classroom was interesting. The children were on a rainy day
schedule and there were some adjustments through the day because of this. Throughout my time
in the cla
FINITE ELEMENT ANALYSIS OF COUNTERSUNK COMPOSITE
BOLTED JOINT IN DOUBLE LAP SHEAR
_
A Thesis
Presented to the
Faculty of
San Diego State University
_
In Partial Fulfillment
of the Requirements for the Degree
Master of Science
in
Aerospace Engineering
_
by
Spring 2001
Complete Solutions
Limits, Continuity, and the Derivative
The regular solutions provide relatively complete solutions except for Problem 9.
9. The definition of the derivative is given by f (x + h) - f (x) . h0 h lim a. For f (x) = x3 , we hav
Fall 2003
Complete Solutions
Introduction to Differentiation
2. From Example 2 of the Worked Examples section on the growth Paramecium caudatum, we have the following table. week 0 2 3 4 5 individuals 2 10 10 11 21 week 6 7 8 9 10 individuals 56 104 137 1
Spring 2008
Complete Solutions
Applications of the Derivative
2. y = x3 12x, y-intercept: y(0) = 0, so (0, 0). x-intercepts: x3 12x = x(x2 12) = x(x+2 3)(x2 3) = 0, so x = 0 and x = 12 = 2 3. No asymptotes Derivative: y (x) = 3x2 12 Critical points satisf
Spring 2010
Math 121a
Name
Give your answers to at least 4 signicant gures whenever possible.
1. (20pts) Dierentiate the following functions (you dont have to simplify):
4
a. f (t) = 2(t2 e2t )3 + 3 ln(t2 + 4) .
t
f (t) =
b. g (x) =
e2x
2
+ (x2 + 3)ex 2x.
Spring 2013
Complete Solutions
Review Exam 3
1. a. Write f (x) as powers of x as much as possible (remove denominators), so
f (x) = 6x3 + 2x2 e2x (x2 9).
Apply power rules, product rule, and the rules for exponential yielding
f (x) = 6(3x2 ) + 2(2x3 ) e2x
Spring 2013
Math 121
Practice Lab Exam 3
Give all answers to at least 4 signicant gures.
1. Over the summer a group of ecology graduate students collects data from a number of sample
plots on insect populations infecting a particular crop. Below is a tabl
Spring 2013
Math 121
Practice Lab Exam 3 Solutions
1. a. The best tting model to the data is given by
P (t) = 0.05039t4 1.335t3 + 9.144t2 2.699t + 51.38.
b. The derivative is given by
dP
= 0.20156t3 4.005t2 + 18.288t 2.699.
dt
c. The relative minima are (
rS
J
J
l
A
Math 121a
Name K e Z
Give your answers to at least 4 signicant gures whenever possible.
Spring 2010
1. (20pts) Dierentiate the following functions (you dont have to simplify):
a. f(t) = 2(t2 - calf + 31n(t2 + 4)
x/E
-2}. 2 at 9/1
w
Spring 2001
Complete Solutions
Allometric Modeling
1. a. If ea = 3.7 and eb = 0.4, then (e0 + ea )2 ea-b = = = eb (1 + ea )2 ea 0.4(1 + 3.7)2 3.7 0.4(4.7)2 = 2.3881. 3.7
b. If ln(c) = -1.5 and ln(d) = 2, then ln(d2 /c) - ln(e) (ln(cd) + ln(1) = = = ln(d2
Math 121
Algebra Self-Test - Complete Solutions
Spring 2001
If you feel that my solutions are omitting too many steps, then you are probably unprepared for Math 121. You should know all steps for solving these problems. 1. From the equation 4x 3 = 7 x, we
Spring 2004
Complete Solutions
Chain Rule
2. The function f (x) = x2 (x3 - 2x + 1)3 is the product of two functions with the second requiring the chain rule. The derivative of f2 (x) = (x3 - 2x + 1)3 is f2 (x) = 3(x3 - 2x + 1)2 (3x2 - 2). By the product r
Ariana Solis
Leadership Book Review
References
Maxwell, J. C. (2009). The right to lead: Learning leadership through character and courage. Naperville:
Simple Tuths.
I choose the book, The right to lead, because I found the title intriguing and I also loo