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04-02-25 06:18 AM |
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Main - General Forum - Here, I shall post problems for others to attempt. |
Kironide |
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Normal User
![]() Paragoomba Level: 21 ![]() ![]() ![]() ![]() Posts: 49/77 EXP: 46978 Next: 2965 Since: 01-07-12 Last post: 3599 days Last view: 3473 days |
f(x) is a differentiable function and g(x) is a doubly differentiable function such that |f(x)| <= 2 and f'(x) = g(x). If [f(0)]^2 + [g(0)]^2 = 9, prove that there exists some c in (-3, 3) such that g(x), g''(c) < 0.
A ray of light traveling in air is incident at grazing angle (incident angle = 90 degrees) n a long rectangular slab of a transparent medium of thickness t = 1.0 m. The point of incidence is the origin A(0,0). The medium has a variable index of refraction ny) given by n(y) = [ky^(3/2)+1]^(1/2) where k = 1.0 (meter)^(-3/2). The refractive index of air is 1.0. Obtain an equation for the trajectory y(x) of the ray in the medium. Is there a strictly increasing function f : R -> R such that f'(x) = f(f(x)) for all x? |
Gohan |
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Normal User
![]() ![]() ![]() Level: 131 ![]() ![]() ![]() ![]() Posts: 1436/5269 EXP: 26135192 Next: 289428 Since: 06-19-12 Last post: 3170 days Last view: 3064 days |
0. Did I win anything? I am just shooting from the hip on this one, I just saw a bunch of numbers. Usually tricky problems end up being 0, so.. |
SapphireBlaze |
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Normal User
![]() ![]() ![]() ![]() ![]() ![]() I may or may not be back to life. Level: 53 ![]() ![]() ![]() ![]() Posts: 27/661 EXP: 1147273 Next: 9846 Since: 10-09-12 From: 51.41277327819231 0.7888535549864173 Last post: 2748 days Last view: 2352 days |
I'm not even going to try to comprehend that. ____________________ |
Main - General Forum - Here, I shall post problems for others to attempt. |
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