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Calculus (1003) Homework 2
发布时间：2022-09-21
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Calculus (1003) Homework 2
September 13, 2022
● Show all steps of your work.
● Solution sheets should be neat and stapled.
Section 2.1
1. If a rock is thrown upward on the planet Mars with a velocity of 8m/s, its height in meters t seconds later is given by y = 7t - 1.86t2 .
(a) Find the average velocity over the given time intervals:
(i) [1, 1. 1|
(ii) [1, 1.01|
(iii) [1, 1.001|
(b) Estimate the instantaneous velocity when t = 1.
Section 2.2
2. For the function A whose graph is shown, state the following.
(a) lim A(x)
x→2-
(d) lim A(x)
x→2＋
(e) lim A(x)
(f) The equations of the vertical asymptotes.
Figure 1: Function A(x).
3. Sketch the graph of the function and use it to determine the values of a for which x(l)
f (x) exists.
-x
(2 - x
if x < -1
if - 1 ≤ x < 1
if x ≥ 1
(1)
Section 2.3
4. Given that
x→2
(c) lim^f (x)
(d)x(l)
(e)x(l)
(f)x(l)
.
5. Evaluate the limit, if it exists.
(a) lim ^u3＋3u＋6
(b) t 
m-3 
(c)h(l)
(d) x
m-2 
(e) lim(2x＋二x - 3二)
6. Let
．x if x < 1
g(x) = 
．(x - 3 if x > 2
(a) Evaluate each of the following, if it exists.
(i) lim g(x)
x→ 1-
(b) Sketch the graph of g.
7. Show by means of an example that x(l)
[f (x)＋g(x)| may exist even though neither x(l)
f (x) nor x(l)
g(x) exists.
