Limits III
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Mathematics 53 2nd Semester, A.Y. 2014-2015 Exercises 3 - Limits III Q3, R3, W8, X8 I. Evaluate the following limits, if they exist. 1. lim y→+∞ (-y 5 +6y 4 +3y 2 - 3) 2. lim x→+∞ x 3 - 4x 7 +5x 3 +1 8x 2 +3x 3 +8x 6 3. lim x→-∞ x 3 +4 6x 8 +9x 4 + x 3 - 1 4. lim x→+∞ 2x 7 +4x 6 - 9x 5 +5x 4 - 2 3+4x - 6x 5 +2x 7 5. lim x→-∞ -2x 7 +3x 2 - 3 x 4 + x 2 +1 6. lim x→+∞ 5x 5 +6x 2 +3 -4 - 5x 5 +4x 3 7. lim u→+∞ ( √ u 2 + 10u - u) 8. lim s→-∞ ( √ 4 - s + s 2 + s) 9. lim x→+∞ (2x - 1+ √ 4x 2 + 1) 10. lim t→-∞ t - √ 4t 2 +1 6t - 7 11. lim x→-∞ √ 8x 2 - 5x - 3 2x +3 12. lim x→-∞ √ x 2 +4 - 4x x - 2 13. lim x→-∞ 1 - 6x √ 9x 2 +1 - 2x 14. lim y→-∞ p 4y 2 + y + y 4y + p y 2 +1 15. lim w→-∞ √ 9w 6 - 4w 4 +8 4w 3 - 3w +1 (Hint: √ w 6 = |w 3 |→-w 3 as w → -∞) II. Challenge! (If you have spare time...) 1. If f (x)= x n + x n-1 + ··· + x + a x m + x m-1 + ··· + x + b (n, m are positive integers, a 6= b), evaluate lim x→+∞ 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 lim x→+∞ ( √ x 2 + ax - x). Exercises from sample exams, books, and the internet rperez
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Exercises in Limits
Transcript of Limits III
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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
