[SOLVED] MA1023 Homework 1

HW 1, MA 1023 Due 1/24

Find the limits in Exercises 1-4.

1.

sin(x²)                                      3x³ +3

1)xlim→0     x                          2)xlim→−1 4x3₋x +3

2.

5x2−3x                                   ex +x2

1)xlim→∞ 7x2 +1        2)xlim→∞ ex +x

3.

1) lim x²lnx         2) lim x²(lnx)² x→0+             x→0+

4.

xe^x                                                 3x +1        1

1)lim ex−1          2)xlim→0+( x − sinx) x→0 Evaluate the integrals in Exercises 5-8.

5.

Z ^∞                                                     Z 2

1                                            2

1) 0 x +2dx                           2) −∞x2 +1dx

6.

Z 1                                                Z 4

1    1 1) √ dx        2) √      dx

0        x                                0         4−x

7. Z _∞

2x

dx

8.

Z 1

1 1 dx

−8x3