Question

Which of the following is true? Multiple answers: You can select more than one option ОА x^3 =Big-Theta(x^4 + x^3) B x^4 =Big-Theta(x^3 + x^4) O с x^3 =Big-Theta(x^3 + 4x +17) O D x^3 + 4x +17 =Big-Theta(x^3) o E 3^n = Big-Theta(2^n) O F 2^n =Big-Theta(3^n)

Answer 1

sol:- 1) For calculating o notation of a function If f(x) is a sum of several terms, if there is one with largest growth rate, it can be Kept, and all others omitted. If f(x) is a Product of several factors, any constants can be omitted .

for the function achta 3 ac the Big-Theta notation is x4 x4+x² . Big. Theta (504) is correct But not 4 Big theta (12) so, option - 0 B arve false for the function, 3 tuxt17 the Big -Theta notation is 3 20 tuxt 17 - Big-Theta (x 3) is correct But not *3 Big-Thetal x? + 4x+14) x So, option - © is false and D is True option- Now, know that ER then lim f(n) nost gen) fon) = Big - Theto (g(n) Now, n lim (²) 29 how to

So, option - © is false from со е have h lim fin gen) im 2 woles n too nosto n lim nato so option is false ง Among 100 people, there are atleast 8 of them born on each month. It is false. proof :- Say 8 were born in January, & in February so on through december. and so that makes 8412 = 96 people, The 97th person must have been born in some month. So that month has 841aq birthday so, Among 100 people, there should be atleast a them born each month.

3)

The divisibility rule of 4 is that the last two digits of the number should be divisible by 4.