# hard

1. ### Hard PDE

Solve \frac{\partial Z }{\partial x} =2x\cdot (1-\frac{\partial Z}{\partial y})\; , for Z(x,0)=Z(0,y)=1 .
2. ### Hard inequality

Given a,b,c>=1 and a+b+c=9. Prove that (âˆša+âˆšb+âˆšc)^2>=ab+bc+ca.

4. ### Hard Limit

Evaluate the limit without L'hÃ´pitalâ€™s rule. \lim_{y\rightarrow \infty }\frac{\ln(yn)}{y^n } \; , n\in \mathbb{N}.
5. ### Hard problem

Evaluate L(s)=\lim_{n\rightarrow \infty } s^{n} \: , s\in \mathbb{R}^{+} .
6. ### Hard limit

Evaluate \lim_{x\rightarrow \infty } e^{-x} \cdot x^{n} \; ; n-positive integer .
7. ### Tennis court surfaces.

https://en.m.wikipedia.org/wiki/Tennis Tennis is played using the following ground surface viz Grass, Hard & Clay surfaces. Which could be considered among the three as the most difficult and most easy court surface to play? Thanks & Regards, Prashant S Akerkar
8. ### A simple Proof by the Easy Or Hard Way?

Given the equations below prove that v^2 = v_0^2 + 2a(x-x_0) 1) v = v_0 + at 2) x-x_0 = v_ot + \frac{1}{2}at^2 Easy Solution: v = v_0 + at \Leftrightarrow t = \frac{v-v_0}{a} Substituting t into equation 2 \Delta{x} = v_0\frac{v-v_0}{a} +...
9. ### Hard Inverse function f(x) problem

So I have this problem f(x)=x^3+x+1 and I need to find the inverse of this function.I know that you have to use differentiation but the problem is I see this solution (f^-1)(3)=1 but I don't understand the steps to reach that conclusion.There was another one (f^-1)(3)=5 and this looked the same...

12. ### Need help in hard exercise

Settle, whether there exist in pairs different rational numbers, such that polynomials have a common irrational element.
13. ### Riemann's Sum Problem

Brief Overview What I've done so far: The Question If the safety capacity for the benign use of a camping gas lamp inside a confined space is (104Ã·5) m^3, calculate whether it would be safe to use the lamp within the lightweight â€˜pop-upâ€™ tent. I know the height of my tent is...
14. ### How to solve this problem? (HARD)

A giant rabbit is tied to a pole in the ground by an infinitely stretchy elastic cord attached to its tail. A hungry flea is on the pole watching the rabbit. The rabbit sees the flea, jumps into the air and lands one kilometre from the pole (with its tail still attached to the...
15. ### Light Hard Drives Question

http://fav.me/dbw3yek how far do I have to place the holograms for optimal capacity?
16. ### Help for the hard prove question

If n is a positive integer and n is even, prove: (2^(n!)-1) is divisible by (n^2-1). This question confuse me some days. Please help me or give me some hint. Thank you very much.
Made errors in earlier posts. This is my question. I have been trying to solve this since summer. It is a question from the book: 7th edition Adams calculus. 2.1.3 Using Newton quotient to solve the problem (not any chain rule, power rule or l'HÃ´pital's rule is allowed). If the function $f$...