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 2 + 1 ) / ( x + 1 ) is O ( x ) .
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 2 + 1 ) / ( x + 1 ) is O ( x ) .
Express the solution of the given IVP in terms of a convolution
where g(t) is an arbitrary function.
Suppose that ƒ(x) = x2 and g(x) = | x | . Then thecompositions( ƒ ∘ g)(x) = | x | 2 = x2 and (g ∘ ƒ)(x) = | x2| = x2 are both differentiable at x = 0 even though g itself is not differentiable at x = 0. Does this contradict the Chain Rule? Explain.
Find the global maximum and global minimum of f(x)=2x in the interval [−1,3].
Chapter 3 Solutions
Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
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