Does limit exist as x approaches zero? Frobenius Method DEQ

[lonewolf219]

Homework Statement

what is the limit of (4x^2-1)/(4x^2)
when x→0

Homework Equations

In order to find the Indicial Equation, do I need to take the limit of p(x) and q(x), the non-constant coefficients? If so, can the limit of this function be found using LH Rule?

The Attempt at a Solution

Please let me know any info you might have about the Frobenius Method, since I am just learning it from my professor's brief notes about it...

 

[LCKurtz]

Homework Statement

what is the limit of (4x^2-1)/(4x^2)
when x→0

What do you think? What have you tried?

 

[lonewolf219]

Well, can you use L' Hopital's Rule twice? (8x - 0)/(8x) and then (8/8) = 1 ?

But I'm confused if I need to multiple by x^2 to find q(nault)?

x^2*q(x)=q(nault)

y''(x) + p(x)y'(x) + q(x)y(x) = 0

If so, would the limit be -1/4?

x^2(4x^2-1)/(4x^2) = [(4x^4)/4x^2] - [x^2/(4x^2)] = [x^2] - [1/4] = [x=0] = - 1/4

 

[HallsofIvy]

L'Hopital applies only when the numerator and denominator both go to 0. Here, if x= 0, the numerator is -1 but the denominator is 0. Suppose x were some very small number, say x= 0.000001. What would that fraction be? Now, what do you thing the limit is?

 

[lonewolf219]

negative infinity, right?