Write the microscope equation for each of the following functions at the indicated point. (To find the necessary derivative, consult problem 2.)

a) f(x)=1/x at x = 2.

d) f(x)=2x at x = 5.

11. This question uses the microscope equation for f(x)=1/x at x = 2 that you constructed in the previous question.

a) What you would see in the microscope if the field of view is .2 units wide.

b) If we take x = 2.05, what is ∆x in the microscope equation? What estimate does the microscope equation give for ∆y? What estimate does the microscope equation then give for f(2.05) = 1/2.05? Calculate the true value of 1/2.05 and compare the two values; how far is the microscope estimate from the true value?

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