Question

determine the following limit.
\\(\lim_{t\to\infty}(- 19t^{-5})\\)
select the correct answer and, if necessary, fill in the answer box to complete your choice
a. \\(\lim_{t\to\infty}(- 19t^{-5})=\square\\)
b. the limit does not exist and is neither -\\(\infty\\) nor \\(\infty\\).

Explanation:

Step1: Rewrite the function

We know that $t^{-5}=\frac{1}{t^{5}}$, so $- 19t^{-5}=-\frac{19}{t^{5}}$.

Step2: Apply the limit rule

As $t
ightarrow\infty$, we consider $\lim_{t
ightarrow\infty}\frac{1}{t^{n}} = 0$ for $n>0$. Here $n = 5>0$, so $\lim_{t
ightarrow\infty}-\frac{19}{t^{5}}=-19\lim_{t
ightarrow\infty}\frac{1}{t^{5}}$. Since $\lim_{t
ightarrow\infty}\frac{1}{t^{5}} = 0$, then $-19\lim_{t
ightarrow\infty}\frac{1}{t^{5}}=0$.

Answer:

A. $\lim_{t
ightarrow\infty}(-19t^{-5}) = 0$