The point P(4, -2) lies on the curve y = 2/(3 - x). (a) If Q is the point (x, 2/(3x)), 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) 3.9 mpQ = (ii) 3.99 mpQ = (iii) 3.999 mpQ = (iv) 3.9999 mpq = 4.1 mpQ = (vi) 4.01 mpQ = (viii) (vii) 4.001 mpQ = mpQ = 4.0001 (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(4, -2). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(4, -2).
The point P(4, -2) lies on the curve y = 2/(3 - x). (a) If Q is the point (x, 2/(3x)), 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) 3.9 mpQ = (ii) 3.99 mpQ = (iii) 3.999 mpQ = (iv) 3.9999 mpq = 4.1 mpQ = (vi) 4.01 mpQ = (viii) (vii) 4.001 mpQ = mpQ = 4.0001 (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(4, -2). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(4, -2).
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(4, -2) lies on the curve y = 2/(3 - x).
(a) If Q is the point (x, 2/(3x)), 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) 3.9
mpQ =
(ii) 3.99
mpQ =
(iii) 3.999
mpQ
(iv) 3.9999
mpq =
E
=
4.1
mpQ =
(vi) 4.01
mpQ =
(viii)
(vii) 4.001
mpQ =
mpQ =
4.0001
(b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(4, -2).
m =
(c) Using the slope from part (b), find an equation of the tangent line to the curve at P(4, -2).
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