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(-3x+x^(4)))/(7+8x^(2)+10 x) 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(-3x+x^(4)))/(7+8x^(2)+10 x) Answer:

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Analyze Behavior of Functions: To find the limit of the function as x approaches infinity, we need to analyze the behavior of the numerator and the denominator separately. We will look for the highest power of x in both the numerator and the denominator to simplify the expression.Divide by Highest Power of x: In the numerator, the highest power of x is x^4, and in the denominator, the highest power of x is x^2. To simplify the limit, we can divide both the numerator and the denominator by x^2, the highest power of x in the denominator.Simplify Expression Inside Square Root: When we divide each term in the numerator and the denominator by x^2, we get: lim_(x rarr oo)(sqrt(x^4 - 3x)/x^2) / (7/x^2 + 8 + 10/x)Ignore Terms Approaching Zero: Now we simplify the expression inside the square root in the numerator by dividing each term by x^2: lim_(x rarr oo)(sqrt(x^2 - 3/x)) / (7/x^2 + 8 + 10/x)Simplified Limit Calculation: As x approaches infinity, the terms -3/x and 7/x^2 in the numerator and the denominator, respectively, will approach zero. The term 10/x in the denominator will also approach zero. So we can ignore these terms for the limit calculation.Square Root of x^2: The simplified form of the limit is now: lim_(x rarr oo)(sqrt(x^2)) / 8Limit Calculation Result: The square root of x^2 is x, so the limit simplifies further to: lim_(x rarr oo)x / 8Limit as x Approaches Infinity: As x approaches infinity, the limit of x/8 is also infinity, since the value of x becomes unbounded and there is no other term in the denominator to counteract this growth.Conclusion: Therefore, the limit of the function as x approaches infinity is infinite, which means the limit does not exist (DNE).

Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE). $\newline$ $\lim _{x \rightarrow \infty} \frac{\sqrt{-3 x+x^{4}}}{7+8 x^{2}+10 x}$ $\newline$ 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→∞−3x+x47+8x2+10x \lim _{x \rightarrow \infty} \frac{\sqrt{-3 x+x^{4}}}{7+8 x^{2}+10 x} x→∞lim​7+8x2+10x−3x+x4​​\newlineAnswer:

Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE). $\newline$ $\lim _{x \rightarrow \infty} \frac{\sqrt{-3 x+x^{4}}}{7+8 x^{2}+10 x}$ $\newline$ Answer: