hard

  1. idontknow

    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. A

    Hard inequality

    Given a,b,c>=1 and a+b+c=9. Prove that (√a+√b+√c)^2>=ab+bc+ca.
  3. T

    a "hard" question

  4. idontknow

    Hard Limit

    Evaluate the limit without L'hôpital’s rule. \lim_{y\rightarrow \infty }\frac{\ln(yn)}{y^n } \; , n\in \mathbb{N}.
  5. idontknow

    Hard problem

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

    Hard limit

    Evaluate \lim_{x\rightarrow \infty } e^{-x} \cdot x^{n} \; ; n-positive integer .
  7. P

    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. B

    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. A

    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...
  10. J

    Hard question

    High school hard geometry question please help guys.
  11. J

    Help with High School Maths hard question

    Please help!
  12. P

    Need help in hard exercise

    Settle, whether there exist in pairs different rational numbers, such that polynomials have a common irrational element.
  13. M

    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 (104÷5) m^3, calculate whether it would be safe to use the lamp within the lightweight ‘pop-up’ tent. I know the height of my tent is...
  14. M

    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. N

    Light Hard Drives Question

    http://fav.me/dbw3yek how far do I have to place the holograms for optimal capacity?
  16. G

    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.
  17. D

    Hard probability question. Advanced answers required.

    To start off: I have a number of trials let's say 10000. I have an abstract die with a very high number of sides. Each roll of a die consumes 1 trial. I roll the die every second. My objective: After selecting a number, roll the die less than 10000 times (number of trials) until you get...
  18. R

    Points on a plane

    Let A1, ..., An and B1,..., Bn be sets of points on a plane. Suppose for all points x, D(x, A1) + D(x, A2) + ... + D(x, An) ≥ D(x, B1) + D(x, B2) + ... + D(x, Bn) , where D(x, y) signifies the distance between x and y. Show that the Ai’s and the Bi’s share the same center of mass...
  19. L

    Hard limit problem one variable calculus

    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'Hôpital's rule is allowed). If the function $f$...
  20. K

    Hard problem-Find the exact value

    (Sin7.5°cos7.5°)(sin7.5°+cos7.5°)(sin7.5°-cos7.5°)(tan7.5°)(cot7.5°)=