discrete structures problems 1.Find a limit to show that x(In(x2))3 is O(x2). Simplify when possible to...

discrete structures problems

1.Find a limit to show that x(In(x²))³ is O(x²). Simplify when possible to avoid doing more work than you have to. You will need to use L'Hôpital's rule at least once.

2.Suppose that f is o(g). What is lim(f(n)/g(n)) as n→ ∞?

3.Suppose that algorithm has run-time proportional to log n and takes 1 millisecond to process an array of size 3,000. How many milliseconds will it take to process an array of size 27,000,000,000 ? Hint: what simple relationship is there between the first number and the second number?

Expert Solution

Colby Messinger answered 2 years ago

For the diﬀerential equation x′′ + (o.1)(1 − x2)x′ + x = 0; x(0) = 1,...

For the diﬀerential equation x′′ + (o.1)(1 − x2)x′ + x = 0; x(0) = 1, x′(0) = 0. (a) Rewrite it as a system of ﬁrst order diﬀerential equations in preparation to solve with the vectorized version of a numerical approximation technique. (b) Use the vectorized Euler method with h = 0.2 to plot out an approximate solution for t = 0 to t = 10. (c) Plot the points to the approximated solution (make a scatter plot), make...

Determine the limit of (x² -3) when x tends to 2 using the definition of limit...

Determine the limit of (x² -3) when x tends to 2 using the definition of limit for E= 0.0030

[Discrete math] Show that it is possible to arrange the numbers 1, 2, . . ....

[Discrete math] Show that it is possible to arrange the numbers 1, 2, . . . , n in a row so that the average of any two of these numbers never appears between them. [Hint: Show that it suffices to prove this fact when n is a power of 2. Then use mathematical induction to prove the result when n is a power of 2.] I saw the solution but I don't understand why permutation pi is using here.....

Simplify into one fraction: 3/x + 1/7

f(x) = −x2 + 3x and g(x) = x − 3 Find the area of the...

f(x) = −x2 + 3x and g(x) = x − 3 Find the area of the region completely enclosed by the graphs of the given functions f and g in square units.

For the function y = -x2/3-x a) Find the slope of tangent at x=4 b) find...

For the function y = -x2/3-x a) Find the slope of tangent at x=4 b) find y''

(a) Find the limit of {(1/(n^(3/2)))-(3/n)+2} and use an epsilon, N argument to show that this...

(a) Find the limit of {(1/(n^(3/2)))-(3/n)+2} and use an epsilon, N argument to show that this is indeed the correct limit. (b) Use an epsilon, N argument to show that {1/(n^(1/2))} converges to 0. (c) Let k be a positive integer. Use an epsilon, N argument to show that {a/(n^(1/k))} converges to 0. (d) Show that if {Xn} converges to x, then the sequence {Xn^3} converges to x^3. This has to be an epsilon, N argument [Hint: Use the difference...

find the riemann sum f(x)=x^2 +3x over the interval [0,8] where x0 =o, x1=1 , x2=6,...

find the riemann sum f(x)=x^2 +3x over the interval [0,8] where x0 =o, x1=1 , x2=6, x4=8, and c1=1, c2=2, c3=4, c4=6

Problem 1. Show that the cross product defined on R^3 by [x1 x2 x3] X [y1...

Problem 1. Show that the cross product defined on R^3 by [x1 x2 x3] X [y1 y2 y3] = [(x2y3 − x3y2), (x3y1 − x1y3), (x1y2 − x2y1)] makes R^3 into an algebra. We already know that R^3 forms a vector space, so all that needs to be shown is that the X operator is bilinear. Afterwards, show that the cross product is neither commutative nor associative. A counterexample suffices here. If you want, you can write a program that...

Show that the quotient ring Q[x]/(x2 − 3) is isomorphic to a subfield of the real...

Show that the quotient ring Q[x]/(x2 − 3) is isomorphic to a subfield of the real numbers R.

Question