L’Hospital’s theorem

Indeterminate Forms UHospital s Theorem Forms of the type 0/0, oo/oo, 0 X oo, etc., are callea indeterminates. To find the limiting values that the corresponding functions approach, L Hospital s theorem is useful If two functions/(x) andg(x) both become zero at X = a, then the hmit of their quotient is equ to the hmit of the quotient of their separate derivatives, if the limit exists or is -i- oq or — oo. 

We can check the relative tail weights exactly. Since we have formulas for the target and the starting densities, we can take the derivative of their ratio. Using the limit theorems of calculus and L Hospital s rule we can find limits of this ratio for 0 approaching oo. The candidate distribution has heavier tails if the limits of the ratio are greater than 1. 

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