The point P(2, -1) lies on the curve y = 1/(1-x). (a) If Q is the point (x, 1/(1-x)), use your calculator to find the slope of

Question

The point P(2, -1) lies on the curve y = 1/(1-x).
(a) If Q is the point (x, 1/(1-x)), use your calculator to find the slope of the secant line PQ (correct to six decimal places) for the following values of x:
(ii) 1.9
(iii) 1.99
(vi) 2.1
(vii) 2.01
(i) 1.5
(v) 2.5
(iv) 1.999
(viii) 2.001
(b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(2, -1).
(c) Using the slope from part (b), find an equation of the tangent line to the curve at P(2, -1).

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