Question

Determine the parameter $k \in \mathbb{R}$ such that \begin{equation} \lim_{x \to +\infty} \left( \frac{5x^5 + 3x^2 + \log x}{5x^5 + 3x^2 + \log x - \frac{1}{2}} \right)^{\frac{2}{3}x^7 \sin \frac{4k}{x^2}} = 9 \end{equation} (in the formula $\log$, like $\ln$, denotes the natural logarithm). Write your answer in decimal form to four decimal place (no standard form/scientific notation):

          Determine the parameter $k \in \mathbb{R}$ such that \begin{equation*} \lim_{x \to +\infty} \left( \frac{5x^5 + 3x^2 + \log x}{5x^5 + 3x^2 + \log x - \frac{1}{2}} \right)^{\frac{2}{3}x^7 \sin \frac{4k}{x^2}} = 9 \end{equation*} (in the formula $\log$, like $\ln$, denotes the natural logarithm). Write your answer in decimal form to four decimal place (no standard form/scientific notation):

Determine the parameter k ∈ℝ such that
limx → +∞( (5x^5 + 3x^2 + log x)/(5x^5 + 3x^2 + log x - (1)/(2)))^(2)/(3)x^7 sin(4k)/(x^2) = 9
(in the formula log, like ln, denotes the natural logarithm). Write your answer in decimal form to four decimal place (no standard form/scientific notation):

Added by Ryan W.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Bobby Barnes

Step 1

Therefore, the expression becomes: limxâ†’0 (S1s+log 31 sin %) Show more…

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Determine the parameter k âˆˆ R such that S1s+3x'+log 31 sin % limxâ†’0 = 9 Sxs+3x+log (in the formula log, like ln, denotes the natural logarithm). Write your answer in decimal form to four decimal places (no standard form/scientific notation).