The point P(9, -4) lies on the curve y = 4/(8 - x). (a) If Q is the point (x, 4/(8 - x)), use your calculator to find the slope mpo of the secant line PQ (correct to six decimal places) for the following values of x. (1) 8.9 mpQ = (ii) 8.99 mpQ = (iii) 8.999 mpQ = (iv) 8.9999 mpQ = (v) 9.1 mpQ = (vi) 9.01 mpq = (vii) 9.001 mpQ = (viii) 9.0001 mpq= (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(9,-4). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(9,-4).
The point P(9, -4) lies on the curve y = 4/(8 - x). (a) If Q is the point (x, 4/(8 - x)), use your calculator to find the slope mpo of the secant line PQ (correct to six decimal places) for the following values of x. (1) 8.9 mpQ = (ii) 8.99 mpQ = (iii) 8.999 mpQ = (iv) 8.9999 mpQ = (v) 9.1 mpQ = (vi) 9.01 mpq = (vii) 9.001 mpQ = (viii) 9.0001 mpq= (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(9,-4). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(9,-4).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The point P(9, -4) lies on the curve y = 4/(8 − x).
(a) If Q is the point (x, 4/(8 − x)), use your calculator to find the slope mpo of the secant line PQ (correct to six decimal places) for the following values of x.
-
(i) 8.9
mpQ =
(ii) 8.99
mpQ =
(iii) 8.999
mpQ
(iv) 8.9999
mpq=
(v) 9.1
mpQ =
=
(vi) 9.01
mpQ
(vii)
mpQ
(viii)
=
9.001
=
mpq=
=
9.0001
(b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(9, −4).
m =
(c) Using the slope from part (b), find an equation of the tangent line to the curve at P(9, −4).
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