Questions: Find the given limit. lim x → 3+ (3x^5 - 9x^4 + 8) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. lim (3x^5 - 9x^4 + 8) = □ (Simplify your answer.) x → 3+ B. The limit does not exist and is not ∞ or -∞.

Find the given limit.
lim x → 3+ (3x^5 - 9x^4 + 8)

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. lim (3x^5 - 9x^4 + 8) = □ (Simplify your answer.)
x → 3+
B. The limit does not exist and is not ∞ or -∞.

Transcript text: Find the given limit. \[ \lim _{x \rightarrow 3^{+}}\left(3 x^{5}-9 x^{4}+8\right) \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\lim \left(3 x^{5}-9 x^{4}+8\right)=$ $\square$ (Simplify your answer.) \[ x \rightarrow 3^{+} \] B. The limit does not exist and is not $\infty$ or $-\infty$.

Solution

Solution Steps

To find the limit of the function as $ x $ approaches $ 3^+ $, we can directly substitute $ x = 3 $ into the polynomial $ 3x^5 - 9x^4 + 8 $. Since this is a polynomial function, it is continuous everywhere, and the limit as $ x $ approaches any point is simply the value of the function at that point.

Step 1: Evaluate the Limit by Substitution

To find the limit of the function as $ x $ approaches $ 3^+ $, we substitute $ x = 3 $ into the polynomial $ 3x^5 - 9x^4 + 8 $. Since this is a polynomial function, it is continuous everywhere, and the limit as $ x $ approaches any point is simply the value of the function at that point.

Step 2: Substitute and Simplify

Substitute $ x = 3 $ into the expression: \[ 3(3)^5 - 9(3)^4 + 8 \]

Calculate each term: