determine the following limit.\n\\(\\lim_{t\\to\\infty}(- 19t^{-5})\\)\nselect the correct answer and, if…
determine the following limit.\n\\(\\lim_{t\\to\\infty}(- 19t^{-5})\\)\nselect the correct answer and, if necessary, fill in the answer box to complete your choice\na. \\(\\lim_{t\\to\\infty}(- 19t^{-5})=\\square\\)\nb. the limit does not exist and is neither -\\(\\infty\\) nor \\(\\infty\\).
Answer
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 $t\rightarrow\infty$, we consider $\lim_{t\rightarrow\infty}\frac{1}{t^{n}} = 0$ for $n>0$. Here $n = 5>0$, so $\lim_{t\rightarrow\infty}-\frac{19}{t^{5}}=-19\lim_{t\rightarrow\infty}\frac{1}{t^{5}}$. Since $\lim_{t\rightarrow\infty}\frac{1}{t^{5}} = 0$, then $-19\lim_{t\rightarrow\infty}\frac{1}{t^{5}}=0$.
Answer:
A. $\lim_{t\rightarrow\infty}(-19t^{-5}) = 0$