BC2
Practice 3
Name:___
Show your w rklmethod for all problems. No technology help on this page!
1
3
(1)
x ——+—+3
Find3 3x
q
+y
(2)
FdS3z+2) dz =
(3)
I6(sin(3x)+sec2(2x))
13
+3xC
=
I
V’r:q/t
—cos(3x)
Cf
7
±
CeJ()
71’
/rr
f)
K(a i)
(4)
%43
Find the area bounded by f(x) = x and g(x)
x.
(x)?
_i
(5)
—
ui
—.
1
(Ostebee/Zom,
edition, P. 331.)
The graph of a function 1 created with
parts of circls, is sketched to the right.
‘
2nd
2.0
+--7
-=.
Ii
.0
Let g(x)=f(t)dt.
(a) Find g(4) and ‘(4)
_2
iii
c(t) T(t)
l
0,5
LI
‘
(2
-10
(b) Does g have a tangent line at x = 2?
Justify.
_r
51c
-,
(c) Where on [0, 5] is g concave up?
4
3
0i
c
fr
h
k1(V1I’
iç
(d) Write the equation of the tangent line to g
atx=1. cu;)-17q
,
Gv
\// (x-t
(e) Findtheaveragevalueofg’over[0,4].
(L
—
-
Calculator use ahead! Be sure to show your method clearly.
IMSA
Practice3. 1
S 12
5
o
(6)
Find the average value of
f(x)
=
2eX
+1 over the interval [0, 21.
(Xjy
j
J
(3q
os)
0
(7)
I7152H
Find the area of the region bounded by y = 2— x3 and y = x2
—
5x.
Ikcc p1. x =2,
-‘
/
(8)
Write the equati&&fe tangent line to F(x)
F
(9)
(3)
Find
klt2 + 1 dt at x =3.
RI)
7T
F’x)
=
3i2
1 mn
(No work required.)
dx
6, where k has a local maximum.
sin(2u)du find the x values, 0 x
(10) if k(x) =
Justify. Then find the absolute maximum of k on [0, 6].
,
.
ktx
2 43(x 3)
x!k L€1,
ivi(2*)O
c
io((
4t1
J
(
-j
5
rr/
‘
t
tf1
\\%/
(11)
If f’(x)=x21n(x) andf(1)=3,findf(4).
(q)
-
f(
c/i’
x) d v
I
p
101
11
1Lf
ctL,’rz3J,
IMSA
.
Practice3.2
S 12