Question

evaluate the limit: \\(\lim_{x \to 3} 5x^5 - 6x =\\) question help: video submit question

Explanation:

Step1: Substitute \( x = 3 \) into the function

For the limit \( \lim_{x \to 3} (5x^5 - 6x) \), we can use the direct substitution property of limits for polynomial functions (since polynomials are continuous everywhere). So we substitute \( x = 3 \) into \( 5x^5 - 6x \).

First, calculate \( 5x^5 \) when \( x = 3 \): \( 5\times(3)^5 \). We know that \( 3^5=3\times3\times3\times3\times3 = 243 \), so \( 5\times243 = 1215 \).

Then, calculate \( 6x \) when \( x = 3 \): \( 6\times3=18 \).

Step2: Subtract the two results

Now, we have \( 5x^5 - 6x \) evaluated at \( x = 3 \) as \( 1215-18 \).

\( 1215 - 18=1197 \).

Answer:

\( 1197 \)