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(25x^(4)-28x^(2)))/(3x+5x^(2)) 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(25x^(4)-28x^(2)))/(3x+5x^(2)) Answer:

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Simplify Expression: To find the limit of the given function as x approaches infinity, we should first simplify the expression by dividing the numerator and the denominator by the highest power of x in the denominator, which is x^2.Divide by x^2: Divide both the numerator and the denominator by x^2: lim_(x rarr oo)(sqrt(25x^(4)-28x^(2)))/(3x+5x^(2)) = lim_(x rarr oo)(sqrt(25x^(4)/x^2 - 28x^(2)/x^2))/(3x/x^2 + 5x^(2)/x^2)Simplify Inside Limit: Simplify the expression inside the limit: lim_(x rarr oo)(sqrt(25x^(4)/x^2 - 28x^(2)/x^2))/(3x/x^2 + 5x^(2)/x^2) = lim_(x rarr oo)(sqrt(25x^2 - 28))/(3/x + 5)Approaching Infinity: As x approaches infinity, the terms 3/x and -28/x^2 will approach 0. So we can simplify the expression further: lim_(x rarr oo)(sqrt(25x^2 - 28))/(3/x + 5) = lim_(x rarr oo)(sqrt(25x^2))/(5)Square Root Simplification: The square root of 25x^2 is 5x (since x is approaching infinity, we consider only the positive square root): lim_(x rarr oo)(sqrt(25x^2))/(5) = lim_(x rarr oo)(5x)/(5)Cancel Common Factor: Simplify the expression by canceling out the common factor of 5: lim_(x rarr oo)(5x)/(5) = lim_(x rarr oo)xLimit as x approaches Infinity: The limit of x as x approaches infinity is infinity: lim_(x rarr oo)x = oo

Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE). $\newline$ $\lim _{x \rightarrow \infty} \frac{\sqrt{25 x^{4}-28 x^{2}}}{3 x+5 x^{2}}$ $\newline$ 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). $\newline$ $\lim _{x \rightarrow \infty} \frac{\sqrt{25 x^{4}-28 x^{2}}}{3 x+5 x^{2}}$ $\newline$ Answer: