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
That f(x) = -2x, g(x)= |x + 4|, and h(x)2/x-3.
Evalute the functions for the given values of x:
a)(g º f)(x)
b)(g º f º h)(3)
c)f(7)
Let f(x) – x + 2x+ 3x +4 €Z[x] Then x = -1 is a root for/(x) of
multiplicity
None
Th
Chapter 3 Solutions
Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
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