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(x^(4)-8x))/(2+x+3x^(3)) 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(x^(4)-8x))/(2+x+3x^(3)) Answer:

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Simplify Expression: To find the limit of the given function as x approaches infinity, we need to analyze the behavior of the numerator and the denominator separately and then together. We will start by simplifying the expression by dividing both the numerator and the denominator by the highest power of x in the denominator, which is x^3.Divide by x^3: Divide the numerator and the denominator by x^3. In the numerator, we have a square root, so we will divide the term inside the square root by x^6 (since (x^3)^2 = x^6) to maintain the equivalence. (sqrt(x^(4)-8x))/(2+x+3x^(3)) = (sqrt((x^(4)/x^6)-(8x/x^6)))/(2/x^3+x/x^2+3x^(3)/x^3)Simplify Inside Square Root: Simplify the expression inside the square root and the terms in the denominator. (sqrt((x^(4)/x^6)-(8x/x^6)))/(2/x^3+x/x^2+3x^(3)/x^3) = (sqrt(1/x^2 - 8/x^6))/(2/x^3 + 1/x + 3)Analyze Terms: As x approaches infinity, the terms 1/x^2, 8/x^6, 2/x^3, and 1/x in the simplified expression will approach zero. Therefore, we can ignore these terms for the limit calculation. (sqrt(1/x^2 - 8/x^6))/(2/x^3 + 1/x + 3) becomes (sqrt(0))/(0 + 3) as x approaches infinity.Calculate Limit: The square root of 0 is 0, and 0 divided by any non-zero number is 0. Therefore, the limit of the given function as x approaches infinity is 0.

Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE). $\newline$ $\lim _{x \rightarrow \infty} \frac{\sqrt{x^{4}-8 x}}{2+x+3 x^{3}}$ $\newline$ 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→∞x4−8x2+x+3x3 \lim _{x \rightarrow \infty} \frac{\sqrt{x^{4}-8 x}}{2+x+3 x^{3}} x→∞lim​2+x+3x3x4−8x​​\newlineAnswer:

Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE). $\newline$ $\lim _{x \rightarrow \infty} \frac{\sqrt{x^{4}-8 x}}{2+x+3 x^{3}}$ $\newline$ Answer: