In Problems 15–22 , use the given information to sketch the graph of f. Assume that f is continuous on its domain and that all intercepts are included in the table of values. 18. Domain: All real x , except x = 1; lim x → 1 − f ( x ) = ∞ ; lim x → 1 + f ( x ) = ∞ ; lim x → ∞ f ( x ) = − 2 x −4 −2 0 2 f ( x ) 0 −2 0 0
In Problems 15–22 , use the given information to sketch the graph of f. Assume that f is continuous on its domain and that all intercepts are included in the table of values. 18. Domain: All real x , except x = 1; lim x → 1 − f ( x ) = ∞ ; lim x → 1 + f ( x ) = ∞ ; lim x → ∞ f ( x ) = − 2 x −4 −2 0 2 f ( x ) 0 −2 0 0
Solution Summary: The author illustrates the graph of the function f(x) from the given information.
In Problems 15–22, use the given information to sketch the graph of f. Assume that f is continuous on its domain and that all intercepts are included in the table of values.
18. Domain: All real x, except x = 1;
lim
x
→
1
−
f
(
x
)
=
∞
;
lim
x
→
1
+
f
(
x
)
=
∞
;
lim
x
→
∞
f
(
x
)
=
−
2
43
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at Buffalo
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At least one of the answers above is NOT correct.
The figure shows a hill with two paths, A and B.
(a) What is the elevation change along each path? 400
9400
✓ feet
(b) Which path ascends more rapidly? A v
(c) On which path will you probably have a better view of the surrounding
countryside (assuming that trees do not block your view)? A V
(d) Along which path is there more likely to be a stream?
A V
Note: You can earn 50% partial credit for 2-3 correct answers.
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4)
28. (a) Under what conditions do we say that two random variables X and Y are
independent?
(b) Demonstrate that if X and Y are independent, then it follows that E(XY) =
E(X)E(Y);
(e) Show by a counter example that the converse of (ii) is not necessarily true.
7. [10 marks]
Let G = (V,E) be a 3-connected graph with at least 6 vertices. Let C be a cycle in G
of length 5. We show how to find a longer cycle in G.
(a) Let x be a vertex of G that is not on C. Show that there are three C-paths
Po, P1, P2 that are disjoint except at the shared initial vertex and only intersect
C at their final vertices.
(b) Show that at least two of P0, P1, P2 have final vertices that are adjacent along C.
(c) Combine two of Po, P1, P2 with C to produce a cycle in G that is longer than C.
Chapter 4 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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