Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE). lim_(x rarr oo)(root(3)(30x^(8)-64x^(12)))/(9x^(4)+7) Answer:

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Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE).  lim_(x rarr oo)(root(3)(30x^(8)-64x^(12)))/(9x^(4)+7) Answer:

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Identify highest power: Identify the highest power of x in the numerator and denominator. In the numerator, the highest power of x inside the cube root is x^12, and in the denominator, the highest power of x is x^4. To simplify the limit, we will factor out the highest power of x from both the numerator and the denominator.Factor out x^12: Factor out x^12 from the cube root in the numerator and x^4 from the denominator. The expression becomes: lim_(x rarr oo)(root(3)(x^12(30/x^4 - 64)))/(x^4(9+7/x^4))Simplify cube root: Simplify the cube root of x^12 and cancel out x^4. Since the cube root of x^12 is x^4, we can cancel out x^4 from the numerator and denominator: lim_(x rarr oo)(x^4/root(3)(30/x^4 - 64))/(x^4(9+7/x^4)) lim_(x rarr oo)(1/root(3)(30/x^4 - 64))/(9+7/x^4)Evaluate limit: Evaluate the limit as x approaches infinity. As x approaches infinity, the terms 30/x^4 and 7/x^4 approach 0. Therefore, the expression simplifies to: lim_(x rarr oo)(1/root(3)(-64))/(9) lim_(x rarr oo)(1/(-4))/(9)Simplify final expression: Simplify the final expression. The final expression simplifies to: 1/(-4)/9 -1/36

Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE). $\newline$ $\lim _{x \rightarrow \infty} \frac{\sqrt[3]{30 x^{8}-64 x^{12}}}{9 x^{4}+7}$ $\newline$ Answer:

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Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE).\newlinelim⁡x→∞30x8−64x1239x4+7 \lim _{x \rightarrow \infty} \frac{\sqrt[3]{30 x^{8}-64 x^{12}}}{9 x^{4}+7} x→∞lim​9x4+7330x8−64x12​​\newlineAnswer:

Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE). $\newline$ $\lim _{x \rightarrow \infty} \frac{\sqrt[3]{30 x^{8}-64 x^{12}}}{9 x^{4}+7}$ $\newline$ Answer: