Formula Sheet for Math 151, Exam 1 EXPONENTIAL AND LOGARITHMIC FUNCTIONS ex+y = ex ey , ln(xy ) = ln x + ln y , ln(ex ) = x , ln exy = x y ex , ey (ex )y = exy ln(xy ) = y ln(x) loga x = ln x ln a
= ln x ln y , ax = e(ln a)x ,
eln x = x ,
TRIGONOMETRY sin
318 CHAPTER 3 I DIFFERENTIATION
SOLUTION The average rate of change of fur) over [0, 2] is
fall-J’l0)_7~l_1
i 2 — 0 " 2 - 0 ’ ‘ ‘
Graphically, this average rate of change represents the slope el'the seeant line through the points (2. 7) and (0. l} I
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150 CHAPTER 2 | LIMITS
47. Sketch the graph of a function 3(x) such that
l' z oo, lim = —oo. litn x :00
“19% 3(1) H_3+stx) wast )
SOLUTION
48. Find the points of discontinuity of g(x) and determine the type of discontinuity. where
Ex
cos — form-<1
gm:
l
«CHAPTER 2 | LIMITS
will become clear shortly. Finally. because limp”; fix) = L. there exists a 53 3- 0 such that ifix} — L] < r :1 . F‘-
whenever 0 < ix — cl < 53. Now, let 5 : min(51. 52. 53). Then. for all x satisfyingO < |.r — c| < 5. we have '
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chapter Review Exercises 63
P600
rve. It
(ct From the graphs shown above. it is clear that for each n. the polynomial Putt) has precisely n roots on the interval
[—l. l] andthat—l 5 Pn(x)‘_<1forx E [—l, 1].
am REVIEW EXER
14:440:127
Introduction to Computers for Engineers Lecture 11
Lecturer: Brenda Cortez Recitation Instructors: Yun, Bo, Karthik, Muhammad
1
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General Announcements
HW03 - Questions must be made by no later than this Friday, November 19th EXAM02
Math 151, Spring 2009, Review Problems for Exam 1 Your rst exam is likely to have problems that do not resemble these review problems.
Precalculus
1. Find the domain and range of the following functions. 1 (b) x1+1 (c) (a) 3 x 2 2x 2. Express the set of r
Math 151, Fall 2009, Review Problems for Exam 1 Your rst exam is likely to have problems that do not resemble these review problems. (1) Describe the set S = cfw_x R : |2x 4| > 2 and |x 3| 1 in terms of intervals. (2) Assume that f (x) is a function with