Question

For each of the following pairs of functions f and g (both of which map the...

For each of the following pairs of functions f and g (both of which map the naturals N to the reals R), state whether f is O(g), Ω(g), Θ(g) or “none of the above.” Prove your answer is correct. 1. f(x) = 2 √ log n and g(x) = √ n. 2. f(x) = cos(x) and g(x) = tan(x), where x is in degrees. 3. f(x) = log(x!) and g(x) = x log x.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
For each of the following pairs of functions f and g (both of which map the...
For each of the following pairs of functions f and g (both of which map the naturals N to the reals R), show that f is neither O(g) nor Ω(g). Prove your answer is correct. 1. f(x) = cos(x) and g(x) = tan(x), where x is in degrees.
1. (15 pts total) Prove or disprove each of the following claims, where f(n) and g(n)...
1. (15 pts total) Prove or disprove each of the following claims, where f(n) and g(n) are functions on positive values. (a) f(n) = O(g(n)) implies g(n) = Ω(f(n)) (b) f(n) = O(g(n)) implies 2^f(n) = O(2^g(n)) (c) f(n) = O((f(n))^2)
21.2. Let f(n) and g(n) be functions from N→R. Prove or disprove the following statements. (a)...
21.2. Let f(n) and g(n) be functions from N→R. Prove or disprove the following statements. (a) f(n) = O(g(n)) implies g(n) = O(f(n)). (c) f(n)=?(g(n)) if and only if (n)=O(g(n)) and g(n)=O(f(n)).
1. a True or False? If ∫ [ f ( x ) ⋅ g ( x...
1. a True or False? If ∫ [ f ( x ) ⋅ g ( x ) ] d x = [ ∫ f ( x ) d x ] ⋅ [ ∫ g ( x ) d x ]. Justify your answer. B. Find ∫ 0 π 4 sec 2 ⁡ θ tan 2 ⁡ θ + 1 d θ C. Show that ∫ 0 π 2 sin 2 ⁡ x d x = ∫ 0 π 2 cos...
3. For each of the piecewise-defined functions f, (i) determine whether f is 1-1; (ii) determine...
3. For each of the piecewise-defined functions f, (i) determine whether f is 1-1; (ii) determine whether f is onto. Prove your answers. (a) f : R → R by f(x) = x^2 if x ≥ 0, 2x if x < 0. (b) f : Z → Z by f(n) = n + 1 if n is even, 2n if n is odd.
Find each of the following functions. f(x) = 4 − 4x, g(x) = cos(x) (a) f...
Find each of the following functions. f(x) = 4 − 4x, g(x) = cos(x) (a) f ∘ g and State the domain of the function. (Enter your answer using interval notation.) (b) g ∘ f and State the domain of the function. (Enter your answer using interval notation.) (c) f ∘ f and State the domain of the function. (Enter your answer using interval notation.) (d) g ∘ g and State the domain of the function. (Enter your answer using...
For each of the following pairs of polynomials f(x) and g(x), write f(x) in the form...
For each of the following pairs of polynomials f(x) and g(x), write f(x) in the form f(x) = k(x)g(x) + r(x) with deg(r(x)) < deg(g(x)). a)   f(x) = x^4 + x^3 + x^2 + x + 1 and g(x) = x^2 − 2x + 1. b)   f(x) = x^3 + x^2 + 1 and g(x) = x^2 − 5x + 6. c)   f(x) = x^22 − 1 and g(x) = x^5 − 1.
1a. Find the domain and range of the function. (Enter your answer using interval notation.) f(x)...
1a. Find the domain and range of the function. (Enter your answer using interval notation.) f(x) = −|x + 8|   domain= range= 1b.   Consider the following function. Find the composite functions f ∘ g and g ∘ f. Find the domain of each composite function. (Enter your domains using interval notation.) f(x) = x − 3 g(x) = x2 (f ∘ g)(x)= domain = (g ∘ f)(x) = domain are the two functions equal? y n 1c. Convert the radian...
For f(x) = x^2+6 and g(x) = x^2-5 find the following functions. a.) (f o g)(x)...
For f(x) = x^2+6 and g(x) = x^2-5 find the following functions. a.) (f o g)(x) b.) (g o f) (x) c.) (f o g) (4) d.) (g o f) (4)
Find the derivatives of each of the following functions. DO NOT simplify your answers. (a) f(x)...
Find the derivatives of each of the following functions. DO NOT simplify your answers. (a) f(x) = 103x (3x5+ x − 1)4 (b) g(x) = ln(x3 + x) / x2 − 4 (c) h(x) = tan-1(xex) (d) k(x) = sin(x)cos(x)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT
Active Questions
  • Consider insertsort. Suppose that the input array A has 1% probability to be monotonically decreasing. Show...
    asked 7 minutes ago
  • Your company is thinking of introducing a Bring Your Own Device (BYOD) policy. You have been...
    asked 14 minutes ago
  • Attached is the file GeometricObject.java. Include this in your project, but do not change. Create a...
    asked 16 minutes ago
  • Suppose the number of cars in a household has a binomial distribution with parameters n =...
    asked 19 minutes ago
  • HR needs some information on the new interns put into a database. Given an id, email,...
    asked 40 minutes ago
  • Problem solving strategies Questions years = input("Enter a number of years and I'll tell you how...
    asked 44 minutes ago
  • Calculate ?Hrxn for the following reaction: CH4(g)+4Cl2(g)?CCl4(g)+4HCl(g) Use the following reactions and given ?H?s. C(s)+2H2(g)?CH4(g)?H=?74.6kJC(s)+2Cl2(g)?CCl4(g)?H=?95.7kJH2(g)+Cl2(g)?2HCl(g)?H=?184.6kJ Express...
    asked 51 minutes ago
  • ASCII (American Standard Code for Information Interchange) has an encoding for every character of the alphabet,...
    asked 1 hour ago
  • Is home confinement with electronic monitoring a deterrent? Are there negatives to being confined to one’s...
    asked 1 hour ago
  • Social hostility can have severe lasting effects of interperpersonal relationship during our adolescence years, which if...
    asked 1 hour ago
  • - A series RLC circuit has R=15 ?, L=1.5 H, and C=15 ?F. (a) For what...
    asked 1 hour ago
  • TV Circuit has 30 large-screen televisions in a warehouse in Erie and 60 large-screen televisions in...
    asked 1 hour ago