EVALUATING SIMPLE LIMITS ANSWERS.
Evaluate the following limits We cannot see what these
by simply inspecting the
expressions approach as
expression and see what is h0 because we get 0
left as h approaches zero.
0
which is indeterminate and it
Remember 0 = 0
can equal anything at all.
1
We need to simplify the
but 1 is infinite (ie no limit) expression first.
0
11. lim (4 + h)2 – 16
h0
1. lim 6 + h =
6
h
h0
= lim 16 + 8h + h2 – 16
h
2. lim 4x + 8h = 4x
h 0
= lim h(8 + h)
h
2
2
2
3. lim 5x + 3xh + h = 5x
h0
=8
4. lim 7h
=
0
5 lim
=
0
h0
h0
h
3
6*. Lim 4
h0
h
= no lim
or 
7. lim h2 + 2h + 1 = 1
h0
8. lim 5xh + 6x2 = 6x2
h0
9**. lim
x2
6
no lim
(x – 2) or 
10**. lim h + 3
h0
h
no lim
or 
Estimate these limits by
choosing decreasing values
of h which approach zero.
Be sure you have the limit
correct to at least 3 sig fig.
14. lim
h0
9h – 6h2
3h
If h = 0.1
9h – 6h2
3h
If h = 0.01
9h – 6h2
3h
If h = 0.001
9h – 6h2
3h
If h = 0.0001
9h – 6h2
3h
= 2.8
= 2.98
=2.998
= 2.9998
12. lim (1+h)2+3(1+h) – 4
h0
h
2
= lim(1+2h+h +3 + 3h– 4)
Limit to 3sig fig = 3
h
= lim 5h + h2
15. lim 5h – 2h
h
h0
h
= lim h(5 + h)
If h = 0.001
h
5h – 2h = .91735
h
=5
If h = 0.0001
2
2
5h – 2h = .91639
13 lim (x+h) +4(x+h)–x –4x
h0
h
h
2
2
2
=lim x +2xh+h +4x+4h-x -4x
If h = 0.00001
h
5h – 2h = .91630
=lim h(2x + 4 + h)
h
h
= 2x + 4
Limit to 3sig fig = 0.916