Consider the function 1– cos(x) f(x): (a) (T) Evaluate lim, →0 f(x) = L. (b) (T) As x → 0, at what rate does f(x) → L? (c) Compute f(x) as written on a computer for values of x = 10-1, 1o-2, …, 10–10. Com- ment on your results. (d) Suppose that we are able to represent floating point numbers with N decimal digits of accuracy. Around what value of r will the evaluation of f(x) produce very large relative errors when |x| < r? (e) Rearrange the expression for f(x) to a mathematically equivalent expression so that the this new function evaluates accurately for very small values of x. Verify the success of your rearrangement computationally. Are there values of x where you expect accuracy problems with your rearrangement?

(6) 4. Consider the graph given below of a function, f(x): 2 -1- -2- -3- (a) Evaluate the following (use DNE if the answer does not exist): lim f(r) = lim f(r) = f(-1) = lim f(r) = lim f(x) = f(2) = I+2+ (b) List all points of discontinuity for f (x). 2.

Suppose s(t) = 9 In(+1) is the position of an object measured in centimeters at t seconds. (a) Find the average velocity of the object from t = 6 seconds to t = 16 seconds. Give your answer to two decimal places. -Select-- V (b) Which of the following represents the instantaneous velocity of the object at t = 4? (Select yes or no.) lim 5(4+h)-s(4) 10 h lim s(t+h)-s(t) t-4 h s(4) s(3) 4-3 The slope of the graph of s(t) at t = 4 lim s(t) - s(4) t-4 t-4 -Select--- ♥ --Select-- -Select-- -Select-- ♥ -Select-