Upload
others
View
5
Download
0
Embed Size (px)
Citation preview
IAP GalculusGhapter 3 Test -AB -V2
Differentiate each of the following functions:
1) !=3xs-E*!
[sxQ - *" l t
Name:
2) y=log+(Zxz-x)
l \rAU - CZrl^^) .A'nq
4x-\
t {x- l
ln*
Y : cot( sin x)
St= -.lc'(:unx) cctl>.x
G""^,a)
4)3)
-.l
. l
5) What is the slope of the line tangent to the curve / = tan-1 4x atthe point at which1^^.
* = ;? Show your work.
(A) -z
(D)12
(B)
(E)
.t
L2
2
(c) 0
$--Lt + (.en)'
t \q
---
\ t tb Clq)"
q- ---=
t *,, C' l u)
- ,* =\=^
x=\/+
6) Use the following table of values to calculate the derivative of the given function at
x--2.
x f(x) a(x) f ' (x) a'(x\2 5 4 -3 94 3 2 -2 J
a Qf -lv
-u3
b) f(sQx))
h {'t3 (zx)) . 3'
'27') -}
f ' (3 tz 'z)) ' 3 'A' ' ) '7
?f ' (3C'r)) '3 ' (4) 'a
= { ' tz) Q 3'7-5U7' ,7
=- !S-\q
7) The position of a particle moving on the x-axis at time f > 0 seconds is: x(f) - et - fi
feet.(a) Find the average velocity of the particle over the interval [0,4]'
eu -G - (eo -'6)
?
'|,-- ̂ trn P
7/q-0
aq -L-\Lt
u4 -3= -- +
(b) Assuming that movement to the right is positive, il yhat direction (left or right)
and how fast is the particle moving at t = 1 seconds?
, \ +. \t )."1'v[€)= e- - IL ' '
t8) What is the instantaneous rate of change at x = 3 of the function / given by
=eL
=4
_L l . *t^\nr"t,"
T^G,A
\
is Pr\$'^ ,5o l-
(B)1B
(E) 13t6
I t- \a@z'9
+?' llo
wl+zg-c! - -+
-23=l6t
I f x3 + Zx'y - 4y = 7, then when x = L, y:ax
(B) _B
@-zat' h vz(* d& * s-zx =Q
7F' t Zr"t +ul
4t5 -tA d+ =eclp
\
e)
n\
b:-3 \ 'Y
?
h)-r*
(A) Z2
(D) 0
(c) -3
Zr.'40x
- Lt djl. c[/
di1dx-
4= - 3x'?r nv
L{-4.t
-3-+c-
@\
l *=\' b --- )
} +4VL
- .l_
=T-L
o>-\
10) The twice-differentiable function/is defined for all real numbers and satisfies thefollowing conditions:
/(o) = 2, f '(o) - -Q and /"(o) : 3
The function g is given by g(x) = eo* + f (x) for all real numbers, where a is aconstant. Find g'(0) and g" (0) in terms of a.
t-t--q
' ((r) = Q>o
=A'+
5!
c
' (n7= ^fr
+- f ' ( r)
g" (-0 =
g" [o)
a, e-o* t f t' [r)
=*lxf" r0)=I*9
-t'' J"t
,( _.t
1 1) The graph of the velocity v(t), in feet per second, of a bicycle racing on a straight road,
for 0 < t < 60, is shoivn. Also, given is a table of values for v(r), at 5 second intervals
of time r.
60
<n
40
30
v0
t0
(a) During what intervals of time is the acceleration of the bike positive? Give a
reason for your answer.
tr*
t(seconds)
v(r) (feetper
second)0 0) 1310 t615 2I20 2525 3530 4035 Aa
+L
40 4445 4850 4555 4460 i1
+l
0,'tr) u ts, f)Vl,' Wt( V Ls (tnIl'-
(b) Find the averase accelerstion of the bike, in ft/r, ou., the interval 0 < f < 60.
q? -o qke- = r--
60 -o bO
(c) Find one approximation for the acceleration of the bike, in rc/rr, utt = 30. Show
the computations you used to arrive at your answer.
Y'-T" =,q -71
vto