# difficult

1. ### Difficult intgration by parts

S sin^-1(2x) between 1/4 and 0
2. ### This is difficult as well, don't know where to start

Let u = (u1, u2, u3) be a vector in R 3 . Prove that ||u|| = 0 if and only if u = 0. [Note: the ‘if and only if’ phrase means that you have to prove TWO things - ﬁrstly, that ||u|| = 0 implies u = 0; and secondly, that u = 0 implies ||u|| = 0.]
3. ### Difficult proving algebra

Prove that there are infinitely many pairs of real numbers x and y such that x does not equal y, and x^y = y^x Help please
4. ### difficult problem

Given b>0 and b^2<a then prove there exists c>0 ,such that: (b+c)^2<a I do not know how to start this problem
5. ### difficult stationary points question

the interval is x and y between 0.25pi and 0.5pi (the square thing kind of confused me!) I got ∂u/∂x = siny sin(2x+y) =0 siny = 0 y = 0 ± npi (not in interval so doesn't count ; npi means integer number of pi) OR 2x +y =0 Also, ∂u/∂y = sinx sin(2y+x) =0 Again sinx =0 ; x = 0 ±npi...
6. ### Difficult Integration problem!!

Hi folks I would greatly appreciate some help with this. I have to integrate the following for a project; Integrate ; (a-m/2 ). (1.122 - 0.231(a/b) + 10.55(a/b)2 - 21.71(a/b)3 - 30.382(a/b)4)-m da [/SUP] I know integration by parts, so can I get away with U =(1.122 - 0.231(a/b) +...
7. ### Analysis question- a bit difficult!

For each integer n>=0, let [a_n, b_n] be a closed, bounded interval in R (real numbers) such that a_n <= b_n (a_n is greater than equal to b_n). Suppose that the resulting collection of intervals is pairwise disjoint, that is if n =/ m (n is not equal to m), then the intersection of [a_n, b_n]...
8. ### Difficult Indefinite Integral

A friend of mine (and now I am) is trying to solve this for a high school kid's AP calculus course. I'm not really worried about the limit part but more how you work it into the correct form to get arctan as an answer. Wolfram took away their free step by step solutions and I'm out of tricks of...
9. ### difficult induction problem

Show that if 0 \leq x < n,n \geq 1, and n \in \mathbb{N} then 0 \leq e^{-x} - \left( 1 - \frac{x}{n} \right ) ^n \leq \frac{x^2e^{-x}}{n}. by mathematical induction.​ I suppsoe the best way is to split up the problem into two parts, one for each of the inequalitys. Doing this, I can get the base...

DIFFICULT TRIG PROBLEM. WOULD SOMEONE PLEASE HELP ME!!! (Itwasntme) (Doh) ATTACHED PDF FILE OF THE PROBLEM BELOW... THANK YOU. MUCH APPRECIATED!!
11. ### Solving difficult differential equation

I have the following differential equation which I want to solve for y as a function of x \frac{\partial y}{\partial x}=\frac{C_{1}\left(C_{5}y+C_{6}\right)^{2}}{C_{2}\left(C_{3}y+C_{4}\right)-C_{7}\left(C_{5}y+C_{6}\right)^{6}} where C_{1},C_{2},C_{3},C_{4},C_{5},C_{6},C_{7} are constants...
12. ### Need help proving survivor function (difficult integration/proof)

Hello, I'm looking to prove a specific part of the survivor function. Basically, I need to show that the mean residual life function [m(t)] uniquely defines the distribution of T. I have a solution, but I am not able to follow how the integration process leads to the final answer: Here...
13. ### Difficult Statistics questions

Hello, I am having quite a bit of difficulty with the following questions: I am not sure how the letters will produce poor samples for certain inquiries. Also, I am not sure about question #2 at all. If anyone can point me in the right direction I would greatly appreciate it. Ishihara
14. ### 2 very difficult trig problems

Having an extremely difficult time solving 2 problems. Have posted it as a photo attachment. The first 2 paragraphs & diagram relate to the 1st problem. The last paragraph is for the second problem. For the second problem, I tried using double-angle formula, but I don't know where to go after...
15. ### A more difficult integral, general power formula

Question: Integrate 28-1-16 (int) 0.8((3 + 2 ln(u))^3) du/u My attempt: u = (3 + 2 ln u) du = 2(1/u) = 2/u My guess at this is to divide the whole integral by 2 now since it has been multiplied by 2 in the derivative. resulting in this: 0.4[3 + 2 ln u]/4 I used a Ti-89 and got a very weird...
16. ### Difficult Question Help (Probability/Statistics) Joint Probability Distributions

Hi Guys, Hope everyone is well. I'm wondering if someone can help me with a difficult problem presented during lecture today. Two friends plan to meet to go to a nightclub. Each of them arrives at a time uniformly distributed between midnight and 1am and independently of the other. Denote...
17. ### Difficult Question Help (Probability/Statistics) Joint Probability Distribution

Hi Guys, Hope everyone is well. I'm wondering if someone can help me with a difficult problem presented during lecture today. Two friends plan to meet to go to a nightclub. Each of them arrives at a time uniformly distributed between midnight and 1am and independently of the other. Denote by X...
18. ### Scaling Hamiltonian

Question proposed by my professor: "Scaling: Consider a version of the Newtonian gravitational problem of n + 1 bodies where there is one large central mass at the origin of coordinates with mass M and n smaller masses in orbit with mass m. Think Saturn’s rings. Let G be the newtonian...
19. ### Difficult Question

If peanuts cost $3 per kg and almonds cost$9 per kg, how many kilograms of almonds should be mixed with 4 kg of peanuts to get a mixture that costs \$7.50 per kg? Please answer as soon as possible
20. ### Difficult maximisation problem

We need to find the value of X that maximizes U, U= [(w*X)^(1-a)-1]/(1-a)*[(s*(1-X))^(1-b)-1]/(1-b) where 0<X<1 w>1 s>1 For special cases of a=1, we have as the first term Ln(wX); for b=1 we have Ln(s(1-X) We are allowed to assume w and s are large such that both terms are positive Taking...