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HW 1, MA 1023

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HW 1, MA 1023

Find the limits in Exercises 1-4.
1.
1) lim
x→0
sin(x
2
)
x
2) lim
x→−1
3x
3 + 3
4x
3 − x + 3
2.
1) limx→∞
5x
2 − 3x
7x
2 + 1
2) limx→∞
e
x + x
2
e
x + x
3.
1) lim
x→0
+
x
2
lnx 2) lim
x→0
+
x
2
(lnx)
2
4.
1) lim
x→0
xex
e
x − 1
2) lim
x→0
+
(
3x + 1
x

1
sinx
)
Evaluate the integrals in Exercises 5-8.
5.
1)Z ∞
0
1
x + 2
dx 2)Z 2
−∞
2
x
2 + 1
dx
6.
1)Z 1
0
1

x
dx 2)Z 4
0
1

4 − x
dx
7.
Z ∞
−∞
2x
(x
2 + 4) 3
2
dx
8.
Z 1
−8
1
x
1
3
dx

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