# How do you find #lim (5+6t^-1+t^-2)/(8-3t^-1+2t^-2)# as #t->0#?

Here is the answer :)

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To find the limit of the given expression as t approaches 0, we substitute 0 for t in the expression and simplify:

lim (5+6t^-1+t^-2)/(8-3t^-1+2t^-2) as t->0

Substituting t=0:

(5+6(0)^-1+(0)^-2)/(8-3(0)^-1+2(0)^-2)

Simplifying:

(5+6(0)+(0))/(8-3(0)+2(0))

(5+0+0)/(8-0+0)

5/8

Therefore, the limit of the given expression as t approaches 0 is 5/8.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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