2)
a)
Evaluatethe following integrals.Showyour work.
sin(x)s . cos(x)ndx
f^
;f
. $ir.(vJ(
r-o*cr)
)fry?dJ-&
tt: ca6/
=- Juu-al"d,.= ut
J
o )lvr:F-Bx-:sdx
(
*)
I
_f_
l- krU'-r*
fl
t
I t -lu4.U
\'\ *aIA .
\{ l*t
&r--cakt&
+'-+t:
-$-- ?alrL
Co",/ch$a { katK :
= ((u*,'f-f
{ra*rx{q)
.
)
€ l- f**,n)l
= a,rcs....
/.") +C : e.r,ct4(*'4 K
olfua.
J-h" ")AG)+<
=
= T-fr^(t-)
u,=Qutgf)
&=*
j
L
d^,
L(e(ug){{
3) Let f (x) = ln(3r) - ln(sx). Does / have an inverse?Explain! (If you refer to a criterion or
test, indicate why the test applies. If you refer to the graph of / you must show that your sketch of
tV ,t h *$
lnO r{,'d'uru
8&(*fo-w-*
o {ht ,&t-k
4) The following multiple choiceproblems
will be graded correct answeronly. you
do not need
to show work, and no partial crediiwill
be given. R.".;;G"r
ans\^/erin the answerblock on the
onthese
pases
youalso
wiunotb. ,cor.h.
*"y,*,
["llf::;1fiffi'.i'Jtr
It is strongly recommendedthat you wolk
,Tfffiil
pages
and
"rthese
o,utthe problemsuntil the
correct answeris uniquely
dont iusttry to solvethemby"intuiti,ori'
or "guessing"
- ;;r;;so is likelyto resuli
,,.r:
Eachcorrect anweris worth 6 points,
eachincorrect answeris countedas0
points. (unanswered
questionsarel point' questionsin which
more than one answeris ticked areconsidered
to havebeen
answeredwrongly.)
A)
\,Vhatis the domain of acos(x)?
tr l-r,il E Lo,nla irD E rc,il tr R
.//
B)
Thesetof anpoints
1rt, ilinere f is a realnumberis the a
graphof y =
tr Ue* tr eU, tr xeU*E lln(x)
/,r(;r)
F---.*--',*
Q
tr -h(8e) E 4t2rn(2)E _ttz tr Us
E t!3|gl
D)
E
tr
E)
An antiderivative of
arccos(x -
(* - +)(6-T)
s)@
E. arctan("-s)
rn(s-x+
Evatuate [
Je :*0.
1-l
tr 1V+c l_b.l
i*t
F)
Differentiatef (x) =
(e '- l
"
(*'*r)z-zx then//(l) =
,-*Jk):
E
E 4*c E fi.,
e, _l
2e2,
(e* - t1z
g
(e* -tSz
E
e*
(ex - t)z
!l e l - - - : 2 (e x - t )z
If you are done and havetime left, checkyour
answerson all the problems.Is in each
problem
clear'what your ans\^rer
is? Did you tick the correct boxes
or, ,t. multiple choicequestions?