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Unit test Problem Find the limit as x x approaches positive infinity. \newlinelim⁡x→∞3x−1x2−6= \lim_{{x \to \infty}} \frac{{3x - 1}}{{\sqrt{{x^2 - 6}}}} =

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Determine end behavior of polynomial and rational functionsright chevron icon

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Jeanne's bank account earns interest annually. The equation shows her starting balance of $500\$500 and her balance at the end of three years, $546.36\$546.36. At what rate rr did Jeanne earn interest?\newline546.36=500(1+r)546.36 = 500(1 + r)
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Jeanne's bank account earns interest annually. The equation shows her starting balance of $350 \$ 350 and her balance at the end of three years, $422.78 \$ 422.78 . At what rate r did Jeanne earn interest?\newline422.78=350(1+r)3422.78=350(1+r)^{3}
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A leaky 10-kg10\text{-kg} bucket is lifted from the ground to a height of 14 m14\, \text{m} at a constant speed with a rope that weighs 0.6 kg/m0.6\, \text{kg/m}. Initially the bucket contains 42 kg42\, \text{kg} of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 14 m14\, \text{m} level. How much work is done? (Use 9.8 m/s29.8\, \text{m/s}^2 for gg.) Show how to approximate the required work (in J\text{J}) by a Riemann sum. (Let xx be the height in meters above the ground. Enter xi∗x_i^* as xix_i.)
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A leaky 10−kg 10-\mathrm{kg} bucket is lifted from the ground to a height of 1414 m at a constant speed with a rope that weighs 0.6 kg/m 0.6 \mathrm{~kg} / \mathrm{m} . Initially the bucket contains 4242 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 14−m 14-\mathrm{m} level. How much work is done? (Use 9.8 m/s2 9.8 \mathrm{~m} / \mathrm{s}^{2} for g .)\newlineShow how to approximate the required work (in J) by a Riemann sum. (Let x x be the height in meters above the ground. Enter xi∗∗ x_{i}^{* *} as xi x_{i} )\newlinelim⁡n→∞∑i=1n(98+35.28xi)Δx\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(\boxed{98+35.28 x_{i}}\right) \Delta x\newlineExpress the work (in J) as an integral in terms of x x (in m).\newline∫014(98+35.28x\int_{0}^{14}(98+35.28 x\newlineEvaluate the integral (in J). (Round your answer to the nearest integer.)
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Solve the equation.\newline6w7=98,3046 w^{7}=98,304
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A leaky 10-kg10\text{-kg} bucket is lifted from the ground to a height of 14 m14\text{ m} at a constant speed with a rope that weighs 0.6 kg/m0.6\text{ kg/m}. Initially the bucket contains 42 kg42\text{ kg} of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 14-m14\text{-m} level. How much work is done? (Use 9.8 m/s29.8\text{ m/s}^2 for gg.) Show how to approximate the required work (in J\text{J}) by a Riemann sum. (Let xx be the height in meters above the ground. Enter xi∗x_i^* as xix_i.)
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f(t)={−64t,t=814−t,t=10t2−3t+2,t≠8,10f(2)=□ \begin{array}{l}f(t)=\left\{\begin{array}{ll}-\frac{64}{t} & , \quad t=8 \\ 14-t & , \quad t=10 \\ t^{2}-3 t+2 & , \quad t \neq 8,10\end{array}\right. \\ f(2)=\square\end{array}
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