Check all the statements that are true:

A) The exponential function is the fastest growing of all functions, i. e. every function f is big-O of exec.

B) If p and q are polynomials, then p is big-O of q exactly if the degree of p is less than or equal the degree of q.

C) If f and g are both big-O of h, then so is their sum.

D) If f and g are both big-O of h, then so is their product.

E) If f and g are both of order h, then their sum is of order h as well.

F) If f is of order g, so is 10f.

Question

Nikolai Booth

Mathematics

24 March, 10:49

Check all the statements that are true:

A) The exponential function is the fastest growing of all functions, i. e. every function f is big-O of exec.

B) If p and q are polynomials, then p is big-O of q exactly if the degree of p is less than or equal the degree of q.

C) If f and g are both big-O of h, then so is their sum.

D) If f and g are both big-O of h, then so is their product.

E) If f and g are both of order h, then their sum is of order h as well.

F) If f is of order g, so is 10f.

+5

Answers (1)

Know the Answer?

Ryland Carlson · Answer 1

The true among them are: B, C, E and F

Step-by-step explanation:

A is not true.

f (x) = x^x grows at of an order bigger than e^x

in fact f (x) = 4^x grows faster than e^x

B Is true ... if p is growing more slowly than q then |x^p| x0

C is true

D is not true.

f = O (h) and g = O (h)

fg = O (h^2)

E. Is true

F is true if |f (x) < M |g (x) | then |10 f (x) | < 10M |g (x) | and 10 M is a positive