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Math 141 (Section 04) Practice EXAM 2 (Version 2)
1. Let
f
(
x
) =
e
x
+
x
for all
x
.
a) Justify why
f
has an inverse and Fnd the domain and the range of
f
−
1
.
b) ±ind (
f
−
1
)
′
(1)
.
2. a) Simplify sec(tan
−
1
(
√
x
)).
b) ±ind
f
′
(
x
) if
f
(
x
) = ln(1 + 2
x
), for each
x
.
3. Evaluate the following integrals
a)
i
1
0
e
1+ln
x
√
1+
x
2
dx.
b)
i
4
3
1
x
2
−
6
x
+18
dx.
4. a) ±ind the following limits, justify your answers and clearly identify all indeterminate forms.
(i) lim
x
→∞
x
1
/
2
sin
1
x
.
(ii) lim
x
→
0
+
ln
x
ln(sin
x
)
.
b) Let
f
(
x
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Unformatted text preview: ) = cos x x 2 − π 2 / 4 forπ/ 2 < x ≤ 0. ±ind the value that should be assigned to f (π/ 2) to make the function f continuous on [π/ 2 , 0]. Justify your answer. 5. Consider the following linear Frst order di²erential equation dy dx + y cos x = cos x. a) ±ind the general solution of the equation. b) ±ind the particular solution for which y ( π/ 2) =1. 1...
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This note was uploaded on 09/07/2011 for the course MATH 141 taught by Professor Hamilton during the Spring '07 term at Maryland.
 Spring '07
 Hamilton
 Math

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