Mathematics4students
289
5
9
Hey Math Fans!
In response to frequent requests from students, we structured a fully rigorous, step-by-step resolution that addresses every analytical subtlety of this problem.
Here is our problem statement:
Let f be a continuously differentiable function defined on the positive real numbers, such that f(1)=2.
Suppose f satisfies the condition: the limit as t approaches x of the quantity t squared times f of x, minus x squared times f of t, all divided by t minus x, equals 1, for all x >0
Can YOU evaluate the exact value of f(2)?
For a detailed step-by-step solution, watch MOA Lesson 70, linked below:
https://youtu.be/IUid51tEqwM
Your likes, comments, and subscriptions motivate us to continue creating accessible, rigorous, high-quality, and globally relevant content for our students worldwide.
The Math Olympiad Academy Team
revooms
TORQD
This was written by a virgin robot
TORQD
(Who is also megaloads smarter than me)
QuitLookinAtMineAim
The best way to solve a problem like this is to already know the answer
Mathematics4students
First, turn the limit into a standard linear differential equation form. then find f(x), then replace x by 2 to find the value of f of 2. It is easy.
QuitLookinAtMineAim
It's a Feynman quip he would use in lectures referring to differential equations. Nevermind.
UnattendedDeviant
The exact value of f(2) is 3.
Mathematics4students
No, it is not 3, first solve the problem and turn the limit into a standard linear
differential equation form. then find f(x), then replace x by 2 to find the value of f of 2.
UnattendedDeviant
I did that. Then converted back to standard linear, then did a general solution. Using a initial condition to get 3 my constant violates the boundary condition f(1)= 2.
But I've been smoking a lot of weed tonight so there's that. I'll