The The point P(8, −2) lies on the curve y = 2/(7 − x). (a) If Q is the point (x, 2/(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, −2). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(8, −2)

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