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).
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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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