Exercises 1—14, to establish a big- O relationship, find witnesses C and k such that | f ( x ) | ≤ C | g ( x ) | whenever x > k . Show that ( x 3 + 2 x ) / ( 2 x + 1 ) is O ( x 2 ) .
Exercises 1—14, to establish a big- O relationship, find witnesses C and k such that | f ( x ) | ≤ C | g ( x ) | whenever x > k . Show that ( x 3 + 2 x ) / ( 2 x + 1 ) is O ( x 2 ) .
Solution Summary: The author explains that the given function is O(x2).
Use graphs to determine if each function f in Exercises 45–48
is continuous at the given point x = c.
[2 – x, if x rational
x², if x irrational,
45. f(x)
c = 2
x² – 3, if x rational
46. f(x) = { 3x +1, if x irrational,
c = 0
[2 – x, if x rational
47. f(x) = { x², if x irrational,
c = 1
x² – 3, if x rational
3x +1, if x irrational,
48. f(x) :
c = 4
In Exercises 102–103, find a. (fog)(x); b. the domain of (fo g).
x + 1
* - 2"
103. f(x) = Vx – 1, g(x) = x + 3
102. f(x) =
8(x)
Let f(x) – x + 2x+ 3x +4 €Z[x] Then x = -1 is a root for/(x) of
multiplicity
None
Th
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