EXPLORING CONCEPTS Finding Functions Find differentiable functions f and g such that lim x → ∞ f ( x ) = lim x → ∞ g ( x ) ∞ and lim x → ∞ [ f ( x ) − g ( x ) ] = 25. Explain how you obtained your answers. (Note: There are many correct answers.)
EXPLORING CONCEPTS Finding Functions Find differentiable functions f and g such that lim x → ∞ f ( x ) = lim x → ∞ g ( x ) ∞ and lim x → ∞ [ f ( x ) − g ( x ) ] = 25. Explain how you obtained your answers. (Note: There are many correct answers.)
Solution Summary: The author calculates the differential functions f and g that satisfy the provided condition.
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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S
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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