HW01-solutions

# HW01-solutions - husain (aih243) HW01 Gilbert (56215) This...

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husain (aih243) – HW01 – Gilbert – (56215) 1 This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. Welcome to Quest. Print of this as- signment and bring it to lecture as well as discussion group. 001 10.0 points A tank holds 1000 gallons oF water, which drains From the bottom oF the tank in halF an hour. The values in the table t (min) 5 10 15 20 25 30 V (gal) 657 435 229 134 20 0 show the volume, V ( t ), oF water remaining in the tank (in gallons) aFter t minutes. IF P is the point (15 , V (15)) on the graph oF V as a Function oF time t , fnd the slope oF the secant line PQ when Q = (25 , V (25)). 1. slope = 20 . 9 correct 2. slope = 41 . 8 3. slope = 42 . 8 4. slope = 9 . 5 5. slope = 20 . 6 Explanation: When P = (15 , V (15)) , Q = (25 , V (25)) the slope oF the secant line PQ is given by rise run = V (25) V (15) 25 15 . ±rom the table oF values, thereFore, we see that slope = 20 229 25 15 = 20 . 9 . 002 10.0 points A car slows down and then stops For an extended time. Sketch a graph oF the position oF the car as a Function oF time. 1. time position 2. time position 3. time position 4. time position

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husain (aih243) – HW01 – Gilbert – (56215) 2 5. time position correct 6. time position Explanation: When the position of the car is plotted against time, the slope of the graph indicates the speed of the car, the greater the slope, the greater the speed, and the car is stationary when the slope is zero. Thus of the graphs, only time position has the given properties. 003 10.0 points The point P (1 , 4 5 ) lies on the graph of the function f deFned by f ( x ) = 4 x 3 + 2 x . By calculating the slope of the secant line PQ for the successive points Q ( x, f ( x )) with x = 1 . 1 , x = 1 . 01 , x = 1 . 001 , x = 1 . 0001 , and x = 0 . 9 , x = 0 . 99 , x = 0 . 999 , x = 0 . 9999 , estimate (to 3 decimal places) the slope of the tangent line to the graph of f at P . Correct answer: 0 . 48. Explanation: The slope of the secant line PQ for general points P ( a, f ( a )) and Q ( b, f ( b )) on the graph of f is given by rise run = f ( b ) f ( a ) b a . ±or the given points P and Q these slopes are f (1 . 1) f (1) 0 . 1 = 0 . 461538 , f (1 . 01) f (1) 0 . 01 = 0 . 478088 , f (1 . 001) f (1) 0 . 001 = 0 . 479808 , f (1 . 0001) f (1) 0 . 0001 = 0 . 479981 , and f (0 . 9) f (1) 0 . 1 = 0 . 5 , f (0 . 99) f (1) 0 . 01 = 0 . 481928 , f (0 . 999) f (1) 0 . 001 = 0 . 480192 , f (0 . 9999) f (1) 0 . 0001 = 0 . 480019 .
husain (aih243) – HW01 – Gilbert – (56215) 3 Consequently, to 3 decimal places these slopes approach 0 . 48 as Q approaches P both from the left and the right, so at P (1 , f (1)) slope tangent line = 0 . 48 . 004

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## This note was uploaded on 11/30/2010 for the course M 408c taught by Professor Mcadam during the Spring '06 term at University of Texas at Austin.

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HW01-solutions - husain (aih243) HW01 Gilbert (56215) This...

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