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).
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).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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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
(b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at
(c) Using the slope from part (b), find an equation of the tangent line to the curve at
mPQ = ?
(ii) 7.99
(iii) 7.999
(iv) 7.9999
(v) 8.1
(vi) 8.01
(vii) 8.001
(viii) 8.0001
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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