PRACTICE EXERCTSES - Do these before the lab period. Answers at bottom of page G

Question

PRACTICE EXERCTSES - Do these before the lab period. Answers at bottom of page Given f = 200 x3, a measured value of x is 3.00 and the known error in x is 0.03. What is the % error in f? With the same function as in Question 1, suppose that 0.03 is the standard deviation in the measured x's and 3.00 is the mean of the measured x's. What is the standard delation in f? What is the fractional standard deviation in f? What is the standard deviation in the mean for f if there were 16 readings of x? Given f= 10.0(x - y), with x = 2.0 plusminus 0.1 and y = 5.0 plusminus 0-2, known errors. What is the maximum possible % error in f? Convince yourself that the answer is correct by taking the values of x and y so as to cause a maximum error in f, and checking to see what the error is. What is the absolute error in f? Given the same function as in Question 3, and given that the x and y values are the mean and standard deviation for several readings of x and y, what is the standard deviation in f? How does it compare with the maximum absolute error in f, assuming the errors known (Question 3) ? What is the standard deviation in the mean for f, if there are 100 reading each of x and y? Given f = A cos(x). If the known error in x is Delta x, what is maximum fractional error in f(x)? Around what angle will the error in f be greatest for a given Delta x?

Explanation / Answer

max error happens when x is above its value and y is below f = 10.0 * (2.1 - 4.8)=-27 value is supposed to be f = 10*(2-5)=-30 so absolute error is 3 % error = 3/30 *100= 10% please do rate me :)

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