Problem---k and n are positive integers. Let f(x) = 1/(xk - 1). Let p(x) = (xk - 1)n+1 fn(x), where fn is the nth derivative. Find p(1).
Originally posted by: Smoke0
Problem---k and n are positive integers. Let f(x) = 1/(xk - 1). Let p(x) = (xk - 1)n+1 fn(x), where fn is the nth derivative. Find p(1).
Originally posted by: Smoke0
Problem---k and n are positive integers. Let f(x) = 1/(xk - 1). Let p(x) = (xk - 1)n+1 fn(x), where fn is the nth derivative. Find p(1).
Originally posted by: Smoke0
Problem---k and n are positive integers. Let f(x) = 1/(xk - 1). Let p(x) = (xk - 1)n+1 fn(x), where fn is the nth derivative. Find p(1).
Originally posted by: Smoke0
It's not homework.Heres the answer.
Solution
Answer: (-1)n+1 n! kn.
A routine differentiation.
Let pn(x) = (xk - 1)n+1fn(x). So fn = pn/(xk - 1)n+1. Differentiating, fn+1 = (pn' (xk - 1) - (n+1)kxk-1pn)/(xk - 1)n+2. Hence pn+1(1) = - (n+1)kpn(1). Also p1(1) = -k. Hence pn(1) = (-1)n n! kn.
Can I call you during my test tomorrow?Originally posted by: IKnowNothing
Math...I love it but it is to damn simple.
English...now there is something a bit harder to predict. Unless you study the emotional and reactional factors....never mind....did I say I love math
Dish out a question about quantum theories and relativity. Love debating!
Math is a chain of events leading to the creation of Universal understanding.
Originally posted by: itachi
try proving euler's equation and laplace's theorem (better known as laplace transform) then use that proof to prove the trig identities, laws, rules, and half angle formulas.. (not concurrently).. now thats a b1tch. not that hard, but extremely time consuming.
Originally posted by: Tiamat
Originally posted by: itachi
try proving euler's equation and laplace's theorem (better known as laplace transform) then use that proof to prove the trig identities, laws, rules, and half angle formulas.. (not concurrently).. now thats a b1tch. not that hard, but extremely time consuming.
heeh, I dipped into that in my partial diff eq's class. Definately took a bit of working at. Let's just say one sign error kept me stunned for 2 hrs and 3 sheets of paper :/
Originally posted by: itachi
try proving euler's equation and laplace's theorem (better known as laplace transform) then use that proof to prove the trig identities, laws, rules, and half angle formulas.. (not concurrently).. now thats a b1tch. not that hard, but extremely time consuming.
ok you just hurt my head there..Originally posted by: DrPizza
Hmmmm
Wouldn't you be using the Laplace transform to demonstrate the trig identities, rather than prove them?
It's been a lonnnnnnng time for me, but working backwards, integral came from the derivative, definition of the derivative,... when you're doing lim h->0 (f(x+h)-f(x)) / h, you end up using trig identities to simplify the derivatives of trig functions. So, the tools you're using to prove the trig identities were actually derived from trig identities.
can't say that i know exactly what you're talking about.. but i got an idea. series solutions in ode kept me going for a couple sheets of paper before i realized that i forgot something.heeh, I dipped into that in my partial diff eq's class. Definately took a bit of working at. Let's just say one sign error kept me stunned for 2 hrs and 3 sheets of paper :/
Originally posted by: itachi
try proving euler's equation and laplace's theorem (better known as laplace transform) then use that proof to prove the trig identities, laws, rules, and half angle formulas.. (not concurrently).. now thats a b1tch. not that hard, but extremely time consuming.