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3. The point P(2, -1) lies on the curve y = 1/(1 − x).
(a) If Q is the point (x, 1/(1 − x)), find the slope of the
secant line PQ (correct to six decimal places) for the
following values of x:
(i) 1.5
(ii) 1.9
(iii) 1.99
(iv) 1.999
(v) 2.5
(vi) 2.1
(vii) 2.01
(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).
