Page 226 - DMTH201_Basic Mathematics-1

Unit 7: Limits

7.10 Review Questions Notes

1. Give the properties of Functions in relation to limits.

2. (a) Show that f(x) = e is a continuous function.
x
5
(d) Show that f(x) = e - x 5 is a continuous function.
+ 2
3. By means of graph, examine the continuity of each of the following functions:
(a) f(x) = x + 1 (b) f x) = x + 2
(
x - 2
2
2
(c) f x) = x - 9 (d) f x) = x - 16
(
(
x + 3 x - 4
4. Evaluate the following limits:
(a) lim5 (b) lim 2
xÆ1 xÆ0
2
(c) lim x +4 5 x + 9 7 (d) lim x + 2 x
xÆ1 3 x + 6 x + 3 1 xÆ-2 x + 3 x - 2 2 x
(x k+ ) - 4 x 4 + -
(e) lim (f) lim x - 1 1 x
xÆ0 ( k k + 2 ) x xÆ0 x

2
(g) lim 1 È 1 + x - ˚ 1 ˘ ˙ (h) lim ( x - ( x + 2 ) x - 3 )(x - 3 1 ) 1
xÆ- Í
2
xÆ1 2
Î
x + 1
2
(i) lim x - 4 (j) lim È 1 - 2 ˘
2
1
xÆ2 x + - 2 3 x - 2 xÆ Í Î x - 1 x - ˚ 1 ˙
(k) lim sinx (l) lim x - 2 (a + 1 )x a+ 2
xÆp p - x xÆ a x - a 2
2
5. Find the left hand and right hand limits of the following functions:
(a) f x) = Ì - x + Ï 2 3 if x £ 1 as x Æ 1
(
Ó 3 x - if x > 5 1
2
(b) f x) = x - 1 as x Æ 1
(
x + 1

Answers: Self Assessment

1. (d) 2. (b) 3. (a) 4. (c)
5. (d) 6. (b) 7. (c)

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