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The point P(8, −3) lies on the curve
y = 3/(7 − x).

(a) If Q is the point x, 3/(7 − x)),
use your calculator to find the slope
mPQ of the secant line PQ (correct to six decimal places) for the following values of x.

(i) 7.9
mPQ =


(ii) 7.99
mPQ =


(iii) 7.999
mPQ =


(iv) 7.9999
mPQ =


(v) 8.1
mPQ =


(vi) 8.01
mPQ =


(vii) 8.001
mPQ =


(viii) 8.0001
mPQ =

(b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at
P(8, −3).

m =


(c) Using the slope from part (b), find an equation of the tangent line to the curve at P(8, −3).

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