State the definition of “f(x) is O(g(x))” and use the definition to show that x 2...

Question

Question

State the definition of “f(x) is O(g(x))” and use the definition to show that x 2 + 3x is O(x 3 ).

Please show as much work as possible. Thanks.

engineering Computer-Science

Answer 1

Answer #1

Definition: The function

iff .

---------------------------------------------------------------------------------------------------------

Given,

f(x) = x² + 3x

g(x) = x³

As

So, it is enough to show that x³ grows faster than any other power of x.

Multiply with x on the right hand and then take a constant "c".

Answer 2

Similar Homework Help Questions

Use the definition of the fact that f(x) is O(g(x)) to show that: 1. 7x^2 is...

Use the definition of the fact that f(x) is O(g(x)) to show that: 1. 7x^2 is O(x^2) 2. x^4 + 9x^3 + 4x + 7 is O(x^4) 3. (x^2+1) / (x+1) is O(x) Hint: Try to simplify algebraic expression.
[12 marks] Using the definition of big-O, show that f(x) is big-O of g, where: f(x)...

[12 marks] Using the definition of big-O, show that f(x) is big-O of g, where: f(x) = 2* + 33 and g(x) = 3* Show the details of your work to obtain a full mark.
(a) Let f(x) = 3x – 2. Show that f'(x) = 3 using the definition of...

(a) Let f(x) = 3x – 2. Show that f'(x) = 3 using the definition of the derivative as a limit (Definition 21.1.2). 1 (b) Let g(x) = ? . Show that y that -1 g'(x) = (x - 2)2 using the definition of the derivative as a limit (Definition 21.1.2).

QUESTION 3 To show that f(x) is O(g(x) using the definition of big o, we find...

QUESTION 3 To show that f(x) is O(g(x) using the definition of big o, we find Cand k such that f(x) < Cg(x) for all x > k. QUESTION 4 Finding the smallest number in a list of n elements would use an OU) algorithm.
please show work 2. 20 pts. Use the formal definition of partial derivative to calculate f(x,y)...

please show work 2. 20 pts. Use the formal definition of partial derivative to calculate f(x,y) if f(x, y) = 2xy2.
Find (f o g)(x) and (g o f)(x) and the domain of each 2 f(x) x...

Find (f o g)(x) and (g o f)(x) and the domain of each 2 f(x) x 2, g(x) = 3x -5x - 2 (f o g)(x) (Simplify your answer.)

1.state the shaded area f(x)=cos(x)+5 g(x)=cos(x)+3 #2. state the shaded area f(x)=sqrt x-4 +3 g(x)=-x+7 Show...

1.state the shaded area f(x)=cos(x)+5 g(x)=cos(x)+3 #2. state the shaded area f(x)=sqrt x-4 +3 g(x)=-x+7 Show work as needed. Circle answer. 1. State the shaded area. f(x) = cos(x) + 5 g(x) = cos(x) + 3 2. State the shaded area 1x) = *-4+3 9(4)=-x.7
ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y...

ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y = f'(x) (c) state the domain of f and the domain of f. Find lin tan 4x cos 3x sin 5x X> 12 Find y if y = (3x+5)*(x+4x) (3 Find y' it ya + 10x tanx 7 Let y= (a) Find (6) Find the equation of the tangent line at (74 y' Elf 8 X3 Prove lim (5-) = 4 (a) write the...
1. The definition of a limit says that lim f(x)=L means that for every & >o...

1. The definition of a limit says that lim f(x)=L means that for every & >o there exists a number 8 >0 such that if o < x-al<8, then f (x)-L<£. We have lim(x + 3x - 2) = 8. If < =0.01, find the largest possible value of that will satisfy the definition. Round your answer to the nearest ten-thousandth (that's four spots after the decimal point). If you're having trouble understanding the deltas and epsilons, that's normal. Another...

Show your work using the definition O() (Using the two constants etc). Let f(n) = O(g(n))...

Show your work using the definition O() (Using the two constants etc). Let f(n) = O(g(n)) and g(n) = O(h(n)). Show that f(n) = O(h(n)).