# L' Hopital Rule Problem and MGFs Statistics

## Homework Statement

Hey all, been having some problem with the rule..technique looks right but doesn't agree with wolfram's calc answer. Doing a moment generating function problem.

M(t)=(e^5t-e^4t)/t, Find EX and VARX

## Homework Equations

M'(0)=e(x) and so on..

## The Attempt at a Solution

Okay, this is an indeterminate equation.. thats why I had to use this rule.. But my answer keeps getting 9 while wolfram says 9/2, so I need some help here.

Ok, using quotient rule, differentiating, I get (5e^5t-4e^4t)/t + (e^4t-e^5t)/t^2. Correct me if Im wrong.

I separated the latter part of the equation into ((e^4t-e^5t)/t)(1/t), which then equals to (-1)(1/t)

Therefore, I get (5e^5t-4e^4t-1)/t, which is indeterminate again, differentiating both nominators, i get 9. What have I done wrong?

Ray Vickson
Homework Helper
Dearly Missed

## Homework Statement

Hey all, been having some problem with the rule..technique looks right but doesn't agree with wolfram's calc answer. Doing a moment generating function problem.

M(t)=(e^5t-e^4t)/t, Find EX and VARX

## Homework Equations

M'(0)=e(x) and so on..

## The Attempt at a Solution

Okay, this is an indeterminate equation.. thats why I had to use this rule.. But my answer keeps getting 9 while wolfram says 9/2, so I need some help here.

Ok, using quotient rule, differentiating, I get (5e^5t-4e^4t)/t + (e^4t-e^5t)/t^2. Correct me if Im wrong.

I separated the latter part of the equation into ((e^4t-e^5t)/t)(1/t), which then equals to (-1)(1/t)

Therefore, I get (5e^5t-4e^4t-1)/t, which is indeterminate again, differentiating both nominators, i get 9. What have I done wrong?

Using l'Hospital's rule is much harder than what you need. Just expand the numerator in powers of t and see what you get.

BTW: the correct spelling is l'Hospital (yes, like the place you go to for medical help)---not l'Hopital. It is pronounced low-pee-tall but not spelled that way.

Using l'Hospital's rule is much harder than what you need. Just expand the numerator in powers of t and see what you get.

BTW: the correct spelling is l'Hospital (yes, like the place you go to for medical help)---not l'Hopital. It is pronounced low-pee-tall but not spelled that way.

I stand corrected haha.

Can you elaborate abit on what you mean by expanding the numerator? Is it the expansion of the partial fractions?

Ray Vickson
Homework Helper
Dearly Missed
I stand corrected haha.

Can you elaborate abit on what you mean by expanding the numerator? Is it the expansion of the partial fractions?

I mean: write out the series expansion of exp(5t) - exp(4t) in powers of t.

Oh are you talking about the Taylor's Series?

Ray Vickson
Homework Helper
Dearly Missed
Oh are you talking about the Taylor's Series?