This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Note: Problems 1—8 are worth four points each. 2 .
1. Suppose we know that 6 is an angle in Quadrant III and that tan(6) = 5 . Find the
value of sin(26).
12 6 4 6 12
A. — B —— C ——— D. —— 
13 «1‘3 m 13 5
. . . . 2a: — x2 (
2. Wthl'l of the followmg statements 13/ are true of the function f(:1:) = m ?
I. f(:23) has no xintercepts.
II. f(a:) has no vertical asymptotes.
III. f (ac) has no removable discontinuities.
A. II only E. III only C. I and II only
D. I and III only E. I, II, and III 3. The graph of which of the following functions is the graph of f (3:) shifted down two units, then shifted left two units, then reﬂected over the :caxis, then reﬂected met
the y—axis‘? A. y=—2‘f(1'+2) B. y=~2+f(z2) C. y=2—f(—2—:r) D. y=2—f(2—:z) E. y=—2—f(2—:n) 4. The area and perimeter of a certain rectangle have the same numerical value. Express
its length 2 as a function of its width 4». E. This cannot be done. 5. A current population of 17 mice will double every 10 days. Express the population
of mice t days from now as a function m(t) . AA ma) = 17(2)r‘a B. m(t) = 10(2)”‘
0. m(t) = 10(17)2= D. me) = 17(10)2t E. m(t) = 17(10)é 6. Which of the following statements is/ are true of the function below? 2 x<~1
1
f(a:)= 1*~ —1<a:51
a;
1+ﬁ a:>1 L f (3:) has one jump discontinuity.
II. f (3:) has one inﬁnite disoontinuity.
III. f (at) has one removable diacontinujty. A. I only B. III only C. I and II only D. II and III only E. I, II, and III 7. Evaluate the limit: lim 1 l 1 , _ . — D. — E. 00
A. 0 B 4 C ﬂ 2 1 . .
8. Examine the functions f(a:) = E and g(::;) = 1 + ﬂ . Which one of the functions
listed below DOES NOT have domain (0, oo ) ‘?
I.fg 11% III.gof IV.fog V.f+g
A. I B. II C. III D. IV E. V Note: Problems 9—12 are worth two points each. 9. Which of the following identities are true for all positive values of 3:? 1. ln( ex + 2) = a: + 111(2) 11. (111(1))3 = 31n(a:) 111. (g): = 31 A. II only B. III only C. I and II only
D. I and III only E. I, II, and III
60 10. The function g(a:) = —— 10+ on [0.25] is one—toone. Evaluate 574(8). 1+\/5 A. 1 B. 4 C. 9 D. 16 E. 25 11. Choose the function that is NOT oue—to—one: A. Mm) = 6"” B. h(z) *4: <1«o=x3 rxﬂo=v6 EA all are these functions are oneto—one 12. Determine the value of the constant c for which the following piecewise—deﬁned func
tion is continuous: lvﬁ x>l
ﬂﬂ— l'x
1+0 a:<l
1 1
A~2 B—— .— 2
2 00 D2 E Bonus!l(4 points) 13. Consider the functions below that we analyzed in lecture. How many of the functions
have a vertical asymptote at z = O 7 sin(a:) __ [m]
:5 III. h(2:) w 7 I. m) = :52 cos(%) II. 57(3)) = A.1 B2 0.3 D.0 MAC 2311 — EXAM 1 Free Response NAME SECTION UF lD TEST FORM CODE A YOU MUST SHOW ALL OF YOUR WORK TO RECEIVE CREDITLI 1. Suppose a particle travels in A straight line so that. its position in meters after t
seconds is given by 5(2‘) 2 t — £2 . a) Calculate thc average velocity of the particle during the ﬁrst 2 seconds of it:
motion. Then calculate the average velocity on the interval [2,3]. Include
units with your answer b) Using limits, ﬁnd the instantaneous velocity of the particle when exactly '2
seconds have passed. Include units with your answer. 2. C irclc all intervals below on which Intermediate Value Theorem guarantees a
2
I v 5 root. (zero) of the function = 1 .
— :1: I. (—4, #2) 11. (—2.0) 111.012) IV. (2,4) 3. SOLVE TWO of the. following equations /inequalities for 1?. Write the solutions as
a set in the manner indicated below You may solve all three if you have time for
bonus points. a) W’rite the solution set: log4(.r  2) = log4(2 + l) + 2 b) Write the set of solutions in [0, 27v ): tan(ar) : 25in(.r) (3) Write the solution set in interval notation: NAME SECTION 4. Examine the function f (x) 2 13h}; f(I‘) =_ 33;): f (I) =__ 11331 f (I) =_
lim f(r) =__ lim f(x) =___ lim =__ rm—Q' .r—«>0+ $—>2+ 11392 M) :__ gig M) =r gig f(:r) z b) Sketch the graph of ﬁx) on the axes below. (Consider simplifying the expres—
sion ﬁrst) c) List all values of a: at. which f (:13) is discontinuous, and classify each as a remov
able, jump. or inﬁnite discontinuity. 5. A population of wolves increases so that the number of wolves x years from now is
_:r,
given by the funcrion W(:r) : a( l — e E j" . 21) Write the formula for l’V(I) when a = 2, b = 4, and n = 3. Then calculate its
inverse function W‘l(.r) . b) Write the formula for W(;r) when a = b = n = 1. Then calculate its inverse
function W ‘1 (:r) i c) Sketch the graphs of W(.r) and its inverse on the same axes below for the case
when u = l) = n. = 1 as in part (b) For the sketch, you may assume the domain
of W(:r) is ALL REAL NUMBERS. Label any usymptotes and intercepts ...
View
Full Document
 Fall '08
 ALL
 Calculus, Continuous function, E., ——— D. ——, following piecewise—deﬁned func, inverse function W‘l

Click to edit the document details