# How do you find #lim lnt/(t-1)# as #t->1# using l'Hospital's Rule?

The answer is

We use,

Normally,

This is undetermined

So, we apply L'Hospital's Rule

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To find the limit of ln(t) / (t - 1) as t approaches 1 using L'Hospital's Rule, we first evaluate the derivatives of the numerator and denominator separately.

The derivative of ln(t) is 1/t, and the derivative of (t - 1) is 1.

Now, applying L'Hospital's Rule, we take the limit of the derivatives of the numerator and denominator as t approaches 1:

lim (1/t) / 1 as t approaches 1.

This simplifies to:

lim 1/t as t approaches 1.

Now, plugging in t = 1, we get:

1/1 = 1.

Therefore, the limit of ln(t) / (t - 1) as t approaches 1 using L'Hospital's Rule is 1.

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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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