Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE). lim_(x rarr oo)(sqrt(64x^(8)-23x^(6)))/(5x^(2)+8x^(4)+10) 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)(sqrt(64x^(8)-23x^(6)))/(5x^(2)+8x^(4)+10) Answer:

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Factor out x^8: We are given the limit: lim_(x -> ∞)(sqrt(64x^(8)-23x^(6)))/(5x^(2)+8x^(4)+10) To simplify this limit, we will first factor out the highest power of x in the numerator and denominator.Factor out x^4: In the numerator, the highest power of x inside the square root is x^8. We factor out x^8 from the square root, which is equivalent to x^4 outside the square root. sqrt(64x^(8)-23x^(6)) = sqrt(x^(8)(64-23/x^(2))) = x^4 * sqrt(64-23/x^(2))Rewrite with factored terms: In the denominator, the highest power of x is x^4. We factor out x^4 from each term. 5x^(2)+8x^(4)+10 = x^4(5/x^(2)+8+10/x^(4))Cancel out x^4 terms: Now we rewrite the limit with the factored terms: lim_(x -> ∞)(x^4 * sqrt(64-23/x^(2)))/(x^4(5/x^(2)+8+10/x^(4)))Remove terms with x: We can now cancel out the x^4 terms in the numerator and denominator: lim_(x -> ∞)(sqrt(64-23/x^(2)))/(5/x^(2)+8+10/x^(4))Simplify square root: As x approaches infinity, the terms with x in the denominator approach zero. Therefore, we can simplify the limit further by removing those terms: lim_(x -> ∞)(sqrt(64))/(8)Division of constants: The square root of 64 is 8, so the limit simplifies to: lim_(x -> ∞)(8)/(8)The limit of a constant over a constant is just the division of those constants: lim_(x -> ∞)(8)/(8) = 1

Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE). $\newline$ $\lim _{x \rightarrow \infty} \frac{\sqrt{64 x^{8}-23 x^{6}}}{5 x^{2}+8 x^{4}+10}$ $\newline$ 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). $\newline$ $\lim _{x \rightarrow \infty} \frac{\sqrt{64 x^{8}-23 x^{6}}}{5 x^{2}+8 x^{4}+10}$ $\newline$ Answer: