# How do you find the limit of #(t^2+t-2)/(t^2-1)# as #t->1#?

factorization initially

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To find the limit of (t^2+t-2)/(t^2-1) as t approaches 1, we can substitute the value of 1 into the expression. However, this would result in division by zero, which is undefined. Therefore, we need to simplify the expression before substituting t=1. Factoring the numerator and denominator, we get (t+2)(t-1)/(t+1)(t-1). Canceling out the common factor of (t-1), we are left with (t+2)/(t+1). Now, substituting t=1 into this simplified expression, we find that the limit is equal to 3/2.

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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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