Sketch the graph of an example of a function f that satisfies all of the given conditions. 15. lim x → 0 − f ( x ) = − 1 , lim x → 0 + f ( x ) = 2 , f ( 0 ) = 1
Sketch the graph of an example of a function f that satisfies all of the given conditions. 15. lim x → 0 − f ( x ) = − 1 , lim x → 0 + f ( x ) = 2 , f ( 0 ) = 1
Solution Summary: The author illustrates the possible graph of f(x) in Figure 1.
Mid-Term Review
Find the formula for (f + g)(x).
f(x) = x² - 10x + 25 and g(x) = x² - 10x + 24
(f + g) (x) = [ 2 ]x²
X +
DELL
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Calculus III
May I please have some elaborations on Example 2 part a? Thank you.
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
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