# Math Calc

Find the limit. (If the limit is infinite, enter '∞' or '-∞', as appropriate. If the limit does not otherwise exist, enter DNE.)

lim t-inf (sqrt(t)+t^2)/(9t-t^2)

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1. the limit is -1
Apply l'Hôpital's Rule twice

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2. Divide numerator and denominator by t^2

(sqrt(t)/t^2+t^2/t^2)/(9t/t^2-t^2/t^2) = (1/t^(3/2)+1)/(9/t -1)

lim 1/t^(3/2)=0
t->∞

lim 9/t=0
t->∞

also

lim 1/t^(3/2)=0
t-> -∞

lim 9/t=0
t-> -∞

So

lim (1/t^(3/2)+1)/(9/t -1) =
t-> -∞
(0+1)/(0-1) = 1/ - 1 = - 1

lim (1/t^(3/2)+1)/(9/t -1) =
t-> ∞
(0+1)/(0-1) = 1/ - 1 = - 1

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