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

Therefore, the ratio becomes negative and decreases without bound.

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To find the limit of ((1/t)-1)/(t^2-2t+1) as x approaches 1 from the right (x->1^+), we can substitute the value of 1 into the expression. Doing so, we get ((1/1)-1)/(1^2-2(1)+1), which simplifies to (1-1)/(1-2+1). Further simplification gives 0/0.

To evaluate this indeterminate form, we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator separately, we get (0-0)/(2-2), which simplifies to 0/0 again.

Applying L'Hôpital's Rule once more, we differentiate the numerator and denominator again. The derivative of the numerator is 0, and the derivative of the denominator is also 0. Therefore, we have 0/0 once more.

To continue, we can apply L'Hôpital's Rule repeatedly until we obtain a determinate form. Differentiating the numerator and denominator again, we get 0/0.

Continuing this process, we find that the limit is still indeterminate. Therefore, we need to use an alternative method to evaluate the limit.

One approach is to factorize the denominator. The expression t^2-2t+1 can be factored as (t-1)^2.

Now, we can rewrite the expression as ((1/t)-1)/((t-1)^2).

Substituting 1 into the expression, we get ((1/1)-1)/((1-1)^2), which simplifies to (1-1)/(0^2), resulting in 0/0.

To proceed, we can simplify the expression further by multiplying both the numerator and denominator by t. This gives us (t(1/t)-t)/((t-1)^2), which simplifies to (1-t)/((t-1)^2).

Now, we can substitute 1 into the expression again. We get (1-1)/((1-1)^2), which simplifies to 0/0.

At this point, we can rewrite the expression as 1/((t-1)^2).

Substituting 1 into the expression one more time, we get 1/((1-1)^2), which simplifies to 1/0^2, resulting in 1/0.

Therefore, the limit of ((1/t)-1)/(t^2-2t+1) as x approaches 1 from the right (x->1^+) is undefined or does not exist.

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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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