Questions: Evaluate the limit as x approaches infinity of (x^5 - 1000x^4) Select one: a. x^5 - 1000x^4 b. -999 c. 0 d. infinity

Solution Steps

We need to evaluate the limit \( \lim_{x \rightarrow \infty} (x^5 - 1000x^4) \). As \( x \) approaches infinity, we analyze the growth rates of the terms in the expression. The term \( x^5 \) grows significantly faster than \( 1000x^4 \).

Since \( x^5 \) dominates \( 1000x^4 \) as \( x \) becomes very large, we can conclude that the limit will be influenced primarily by the \( x^5 \) term. Therefore, we can express the limit as:

\[ \lim_{x \rightarrow \infty} (x^5 - 1000x^4) = \infty \]

Final Answer