inequality

1. Proving inequality for all values greater than n0

Hi, I hope someone can help. I'm trying to figure out how to formally prove that $$\log_2(n) - \log_{10}(n) \geq \frac{\log_2(n)}{2^n}$$ I know intuitively that the right-hand side will become 0 for very large values of n, and the left-hand side will be increasing, but I am not sure how to...
2. absolute value and inequality problems

Inequalities and absolute value, Hello everyone, I have done the following questions and would just like to confirm that my answers are in deed correct. I'm a bit paranoid about them. 1) (y/x - x/y) / (5/y - 5/x) just simplify 2) Solve the inequality in terms of intervals: -1 < 2x - 5 < 7...
3. Inequality

Hi all, I am posting this at the pre-university section because I think it is not that difficult. It is probably a simple question but I just do not get it. The following text is from a paper: "We primarily measure bank risk using the z-score ofeach bank, which equals the return on assets...
4. Solving inequalities question #2

Hi, I hope someone can help. I know that I just posted a question a few minutes ago, but I think this post might be more specific to my confusion. So I've been trying to understand why removing the denominator within a rational inequality is fundamentally "bad". I understand that you have to...
5. Polynomial inequality - word problem

Hi, I hope someone can help. I'm trying to solve for the following question: <= "less than or equal to" >= "greater than or equal to" These are my steps: 1. I know that the volume of a rectangle is l x w x h - therefore the inequality to the equation must be x(50 - 2x)(30 - 2x) <= 4000...
6. Graphing inequality type problem?

Hiya. I was given this question on my test prep homework. I have no idea how to even start it. All help is appreciated. "Graph the region 1<x+y<2 in the x,y coordinate plane." Thank you for any help you can give!

Hi, given complex numbers z1,...zn'shob that there exists a subset J of {1,...,n} such that : attached attempt :i tried to use the residue theorem for the function (z-z1)*.....*(z-zn)/z^n on a circle of around the origin
8. Solving inequality

Would someone mind showing me how to solve the following inequality? $\sqrt{10-x} - \sqrt{x} \leq 2$? The answer is supposed to be $x \in [1, 10]$. It's a bit confusing for me (Worried) Thanks in advance!
9. inequality questiosn

what is the range of value of x fr [ e^-2x (-2x+7) ] > 0
10. Can anyone help show proof on this inequality?

Can anyone of you help me on this problem. My attempt: since a<b then 2a<2b. 2a<1/2(a+b) 2b<1/2(a+b) and i added this two it become a<1/2(a+b)<b
11. Proving a complex inequality

$$|e^z -1| \leq e^{|z|} -1 \leq |z|e^{|z|}$$ for all $z \in C$. I tried substituting $e^z = e^x (\cos y + i \sin y)$ and $|z| = \sqrt {x^2 + y^2}$ but after 2 pages of manipulations, I got back where I started, only messier forms. Any hints are appreciated.
12. Inequality Ti-Nspire CX CAS

Anyone know how to solve this on the Nspire CAS? -9/5<-3t+1<-7/4. What is 9t-3
13. Vector Inequality

Hello, Let A = (a_{ij})_{1\le i \le j \le n} \in M_{n \times n}^{\Bbb R} Such that (a_{ij})=\begin{cases} 2, i \ne j \\ 1, i=j \end{cases} Prove that (<Ax,y>^2) \le (<Ax,x> * <Ay,y>) for every x,y \in \Bbb R^n Where <> stands for the standard inner product in the space. I...
14. Absolute value inequality

hello :) Answer: (2, 14/3)-{3} I would appreciate if you show me step by step!
15. SAT Math problem with an inequality

Hello all! I am so stumped by this one SAT math question that I created a MHF account just to ask. I can't figure out how to algebraically solve the dang thing. The question is as follows (this is from the 2016 SAT Sec. 2 #17): -1 < c < b < a < 1 17. Based on the inequality above, which...
16. Polynomial Inequality

x³-3x+2<=0 Using briott-ruffini method I got these results: x'=1 x"=-2 x'"=x' Correct answer: (-oo, -2]U{1}
17. Inequality

4 < x² - 12 ≤ 4x Correct answer: 4<x≤6
18. Inequality with quotient

How to solve it? Correct answer: {-4 < x < -2}
19. Rationalising a negative denominator in an inequality

So, I have the inequality: 3x+4 > 5√3x +6 This works out to: x > (5√3 + 3)/-33 However... the textbook I am working from gives the answer (as a fraction) x < - (5√3 + 3)/33 Have I missed something when dividing by -1? I get that multiplying both sides of the equation by -1 flips the...
20. Trigonometry inequality

how do you solve |sinx| <= sin 2x ? here's what I tried: |sinx| <= sin 2x = 2sinxcosx <=> -2sinxcosx <= sinx <= 2sinxcosx <=> sinx(2cosx-1) <= 0 AND sinx (1+2cosx) >= 0 then it gets complicated and hard work to solve this and get to the simplified form... is there a simpler way to solve it...