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practice-quiz6 - AMS 151(Fall 2009 Joe Mitchell Applied...

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AMS 151 (Fall, 2009) Joe Mitchell Applied Calculus I Practice Problems for Quiz # 6 1. Gasoline is pouring into a cylindrical tank of radius 3 feet. When the depth of the gasoline is 4 feet, the depth is increasing at 0.2 ft/sec. How fast is the volume of gasoline changing at that instant? (give units!) 2. A voltage V across a resistance R generates a current of I = V/R . If a constant voltage of 9 volts is put across a resistance that is increasing at a rate of 0.2 ohms per second when the resistance is 5 ohms, at what rate is the current changing? (give units!) 3. Compute lim t 0 + 1 t - 1 e t - 1 . 4. Compute lim x 1 ln x x 2 - 1 5. Compute lim t π sin 2 t t - π . 6. Which function dominates as x → ∞ : f ( x ) = 0 . 01 x 3 or g ( x ) = 50 x 2 ? 7. Find the global max and global min of the function f ( x ) = 6 x 3 + 18 x 2 - 54 x + 4 over the interval [ - 4 , 4]. Also determine all local mins and local max’s on that interval. Determine on which intervals of ( -∞ , ) the function is increasing/decreasing. Also, determine on which intervals the function is concave up/up and identify any points of
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