Does anyone good in Analytical Geometry and Calculus
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mat_331_calculus_iiifinal__exam.docMAT 331 CALCULUS III FINAL EXAM
1) Suppose that f is one – to – one, f (7) = 3, and
.
8
)
7
(
=
¢
f
Find (a))
3
(
1
-
f
and (b))
3
(
)
(
1
¢
-
f
.2) Sketch the graph of the function
2
+
-
=
-
x
e
y
.3) Find the inverse function of
1
2
1
)
(
+
+
=
x
x
x
f
.4) Solve the equation
17
=
x
e
e
for x.5) Differentiate (a)
t
t
t
f
ln
)
(
2
=
, (b)t
t
e
e
t
g
+
=
1
)
(
, and (c))
arcsin
arctan(
x
y
=
6) Evaluate the limit for (a)
)
3
(
2
3
lim
-
-
®
x
x
e
, and (b))
arctan(
lim
3
x
x
x
-
¥
®
7) Evaluate
ò
+
4
0
2
16
1
dt
t
by substituting t = 4u and changing the limits of integration.8) Evaluate
ò
+
x
dx
2
1
9) Use integration by parts to evaluate
ò
dx
x
x
x
tan
sec
. (Hint: let u = x and dv = secx tanx dx).10) Evaluate
ò
-
2
1
2
1
dx
x
x
. (Hint: let x = secθ and change the limits of integration).11) Evaluate
ò
q
q
q
d
3
5
sec
tan
