15:13
Calculus: Early Transcendentals
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 $:
(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) $.