Mathematics 53 2nd Semester, A.Y. 2014-2015Exercises 3 - Limits III Q3, R3, W8, X8

I. Evaluate the following limits, if they exist.

1. limy+

(y5 + 6y4 + 3y2 3)

2. limx+

x3 4x7 + 5x3 + 18x2 + 3x3 + 8x6

3. limx

x3 + 4

6x8 + 9x4 + x3 1

4. limx+

2x7 + 4x6 9x5 + 5x4 23 + 4x 6x5 + 2x7

5. limx

2x7 + 3x2 3x4 + x2 + 1

6. limx+

5x5 + 6x2 + 3

4 5x5 + 4x3

7. limu+

(u2 + 10u u)

8. lims

(

4 s + s2 + s)

9. limx+

(2x 1 +

4x2 + 1)

10. limt

t4t2 + 16t 7

11. limx

8x2 5x 3

2x + 3

12. limx

x2 + 4 4xx 2

13. limx

1 6x9x2 + 1 2x

14. limy

4y2 + y + y

4y +y2 + 1

15. limw

9w6 4w4 + 84w3 3w + 1

(Hint:w6 = |w3| w3 as w )

II. Challenge! (If you have spare time...)

1. If f(x) =xn + xn1 + + x + axm + xm1 + + x + b (n, m are positive integers, a 6= b), evaluate limx+ f(x) if

(a) n < m (b) n = m (c) n > m

If you really understand this part, you can solve this in less than 30 seconds!

2. If a R, find limx+

(x2 + ax x).

Exercises from sample exams, books, and the internet rperez