Math

QuestionFind the limit: limt0ln(t)\lim _{t \rightarrow 0^{-}} \ln (-t)

Studdy Solution

STEP 1

Assumptions1. We are dealing with a limit problem. . The function is ln(t)\ln(-t).
3. We are looking for the limit as tt approaches0 from the left side, denoted as t0t \rightarrow0^{-}.

STEP 2

First, let's understand what it means for tt to approach0 from the left side. This means that tt is getting very close to0, but is still a negative number.

STEP 3

Now, let's consider the function ln(t)\ln(-t). The natural logarithm function, ln(x)\ln(x), is only defined for x>0x >0.

STEP 4

Since tt is approaching0 from the left side, t-t is a positive number that is getting very close to0. This means that ln(t)\ln(-t) is defined.

STEP 5

As t-t gets closer and closer to0, ln(t)\ln(-t) will get closer and closer to negative infinity.

STEP 6

Therefore, we can conclude that the limit of ln(t)\ln(-t) as tt approaches0 from the left side is negative infinity.
limt0ln(t)=\lim{t \rightarrow0^{-}} \ln (-t) = -\infty

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