Explain why the curve in Example 5 lies on the cylinder x 2 + y 2 = 1 ,as shown in Figure 14.7 Example 5 Limits and continuity consider the function r ( t ) = cos π t i + sin π t j + e − t k for t ≥ 0 . Figure 14.7
Explain why the curve in Example 5 lies on the cylinder x 2 + y 2 = 1 ,as shown in Figure 14.7 Example 5 Limits and continuity consider the function r ( t ) = cos π t i + sin π t j + e − t k for t ≥ 0 . Figure 14.7
Let f be a function whose graph consists of 5 line segments and a semicircle as shown in the figure below.
Let g(x) = √ƒƒ(t) dt .
0
3
2
-2
2
4
5
6
7
8
9
10
11
12
13
14
15
1. g(0) =
2. g(2) =
3. g(4) =
4. g(6) =
5. g'(3) =
6. g'(13)=
The expression 3 | (3+1/+1)
of the following integrals?
A
Ов
E
+
+
+ +
18
3+1+1
3++1
3++1
(A) √2×14 dx
x+1
(C) 1½-½√ √ ² ( 14 ) d x
(B) √31dx
(D) So 3+x
-dx
is a Riemann sum approximation of which
5
(E) 1½√√3dx
2x+1
2. Suppose the population of Wakanda t years after 2000 is given by the equation
f(t) = 45000(1.006). If this trend continues, in what year will the population reach 50,000
people? Show all your work, round your answer to two decimal places, and include units. (4
points)
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