Questions: Determine the following limit. lim as t approaches infinity of (-11 * t^(-3)) Select the correct answer and, if necessary, fill in the answer box to complete your choice. A. lim as t approaches infinity of (-11 * t^(-3)) = B. The limit does not exist and is neither -infinity nor infinity

Determine the following limit.
lim as t approaches infinity of (-11 * t^(-3))

Select the correct answer and, if necessary, fill in the answer box to complete your choice.
A. lim as t approaches infinity of (-11 * t^(-3)) =
B. The limit does not exist and is neither -infinity nor infinity

Transcript text: its at Infinity Question Determine the following limit. \[ \lim _{t \rightarrow \infty}\left(-11 t^{-3}\right) \] Select the correct answer and, if necessary, fill in the answer box to complete your choice. A. $\lim _{t \rightarrow \infty}\left(-11 t^{-3}\right)=$ $\square$ B. The limit does not exist and is neither $-\infty$ nor $\infty$

Solution

Solution Steps

To determine the limit of the function $-11 t^{-3}$ as $t$ approaches infinity, we observe that as $t$ becomes very large, the term $t^{-3}$ (which is equivalent to $\frac{1}{t^3}$) approaches zero. Therefore, the entire expression $-11 t^{-3}$ approaches zero as well.

Step 1: Analyze the Function

The function given is $-11 t^{-3}$, which can be rewritten as $-\frac{11}{t^3}$. As $t$ approaches infinity, the term $t^3$ becomes very large.

Step 2: Evaluate the Limit

Since $\frac{1}{t^3}$ approaches $0$ as $t$ approaches infinity, the expression $-\frac{11}{t^3}$ also approaches $0$.