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The point P(6, −3) lies on the curve y = 3/(5−x). (a) If Q is the point (x, 3 /(5−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) 5.9 mPQ = (ii) 5.99 mPQ = (iii) 5.999 mPQ = (iv) 5.9999 mPQ = (v) 6.1 mPQ = (vi) 6.01 mPQ = (vii) 6.001 mPQ = (viii) 6.0001 mPQ = (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(6, −3). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(6, −3).

The point P(6, −3) lies on the curve y = 3/(5−x). (a) If Q is the point (x, 3 /(5−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) 5.9 mPQ = (ii) 5.99 mPQ = (iii) 5.999 mPQ = (iv) 5.9999 mPQ = (v) 6.1 mPQ = (vi) 6.01 mPQ = (vii) 6.001 mPQ = (viii) 6.0001 mPQ = (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(6, −3). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(6, −3).

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The point P ( 6 , − 3 ) lies on the curve y = 3 / ( 5 − x ) . (a) If Q is the point ( x , 3 / ( 5 − x ) ) , use your calculator to find the slope m P Q of the secant line P Q (correct to six decimal places) for the following values of x . (i) 5.9
m P Q =
◻ (ii) 5.99
m P Q =
◻ (iii) 5.999
m P Q =
◻ (iv) 5.9999
m P Q =
◻ (v) 6.1
m P Q =
◻ (vi) 6.01
m P Q =
◻ (vii) 6.001
m P Q =
◻ (viii) 6.0001
m P Q =
◻ (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P ( 6 , − 3 ) .
m =
◻ (c) Using the slope from part (b), find an equation of the tangent line to the curve at P ( 6 , − 3 ) . ◻

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