QuestionFind the limit as $t$ approaches 0 from the right of $\log(t)$ .

Studdy Solution

STEP 1

Assumptions1. We are dealing with the natural logarithm, denoted as $\log(t)$ , which is equivalent to $\ln(t)$ in some contexts. . We are finding the limit as $t$ approaches $0$ from the positive side, denoted as $t \rightarrow0^{+}$ .
3. We are using the property of limits that states the limit of a function as $x$ approaches a certain value is the value that the function approaches as $x$ gets arbitrarily close to that value.

STEP 2

We need to evaluate the limit of the function as $t$ approaches $0$ from the positive side.
$\lim{t \rightarrow0^{+}} \log (t)$

STEP 3

The natural logarithm of a number between0 and1 (exclusive) is negative, and as the number approaches0 from the positive side, the natural logarithm approaches negative infinity.
Therefore, the limit of $\log(t)$ as $t$ approaches $0$ from the positive side is negative infinity.
$\lim{t \rightarrow0^{+}} \log (t) = -\infty$ This means that as $t$ gets arbitrarily close to0 from the positive side, the value of $\log(t)$ decreases without bound.

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