p1812tut03 - y = ab x which fits the following data, and...

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School of Mathematics and Statistics The University of Sydney PHAR1812 Calculus Tutorial 3 1. ( i ) Find the points corresponding to (0 , 0), ( π/ 2 , 1), ( π, 0) when the graph of y = sin x is modified by stretching in the x -direction by a factor of 3 and in the y -direction by a factor of 2, shifting π/ 2 units right and 1 unit upwards. What is the amplitude and the period of the new curve. ( ii ) Find a formula for a sinusoidal curve with amplitude 7, period 16 and initial phase angle 2 π/ 3. 2. By plotting the points (log x, log y ) verify that there is a power relationship y = ax b which fits the following data, and find a and b : x 11 22 84 140 420 900 f ( x ) 0 . 155 0 . 254 0 . 675 0 . 965 2 . 130 3 . 710
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3. Find a formula for y as a function of x . (Hint: Use log-log paper.) x 10 20 30 40 50 60 100 140 f ( x ) 32 . 1 17 . 0 10 . 3 8 . 2 6 . 2 5 . 6 3 . 2 2 . 3 4. Plot Y = log y against x to verify that there is an exponential relationship
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Unformatted text preview: y = ab x which fits the following data, and find a and b : x . 1 0 . 3 0 . 5 0 . 7 0 . 9 1 . 1 1 . 3 f ( x ) 3 . 0 2 . 4 1 . 8 1 . 5 1 . 2 1 . 0 0 . 8 5. Consider the following data : x 10 20 30 40 50 60 70 80 y . 58 . 80 . 97 1 . 11 1 . 24 1 . 36 1 . 47 1 . 57 By plotting the points ( x,Y = y 2 ), find a formula for y as a function of x. 6. Sketch the curve y = 2 sin(2 x-π ) . Is this function odd or even? 7. Explain why the sum and product of even functions are even, and the sum of odd functions is odd. What can be said about the product of two odd functions? the product of an odd and an even function? the sum of an odd and an even function?...
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p1812tut03 - y = ab x which fits the following data, and...

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