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 $-\infty$.
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Solution

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Solution Steps

To find the limit of the function as x x approaches 3+ 3^+ , we can directly substitute x=3 x = 3 into the polynomial 3x59x4+8 3x^5 - 9x^4 + 8 . Since this is a polynomial function, it is continuous everywhere, and the limit as x 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 x approaches 3+ 3^+ , we substitute x=3 x = 3 into the polynomial 3x59x4+8 3x^5 - 9x^4 + 8 . Since this is a polynomial function, it is continuous everywhere, and the limit as x x approaches any point is simply the value of the function at that point.

Step 2: Substitute and Simplify

Substitute x=3 x = 3 into the expression: 3(3)59(3)4+8 3(3)^5 - 9(3)^4 + 8

Calculate each term:

  • 3(3)5=3×243=729 3(3)^5 = 3 \times 243 = 729
  • 9(3)4=9×81=729 9(3)^4 = 9 \times 81 = 729

Substitute these values back into the expression: 729729+8=8 729 - 729 + 8 = 8

Final Answer

8\boxed{8}

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