Exercises 1—14, to establish a big- O relationship, find witnesses C and k such that | f ( x ) | ≤ C | g ( x ) | whenever x > k . Determine whether each of these functions is O ( x ). f ( x ) = 10 f ( x ) = 3 x + 7 f ( x ) = x 2 + x + 1 f ( x ) = 5 log x f ( x ) = [ x ] f ( x ) = [ 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 . Determine whether each of these functions is O ( x ). f ( x ) = 10 f ( x ) = 3 x + 7 f ( x ) = x 2 + x + 1 f ( x ) = 5 log x f ( x ) = [ x ] f ( x ) = [ x / 2 ]
Find all parameters a ∈ (0, 4] for which the logistic family ga(x) = ax(1 − x) has an attracting 2-cycle. Conclude that there is in fact a period-doubling bifurcation at a = 3.
a. At what time t does the cave's salamander population reach its maximum?
Find the linearization of f(x)=ln(x2-3) at suitably chosen integer near X=2.1.
Then use the linearization to estimate the value of f(2.1).
Chapter 3 Solutions
Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
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