The point P(6,4) lies on the curve y = 4/(5 - x). (a) If Q is the point (x, 4/(5 - 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) 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 = X X X X (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(6,-4). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(6,-4).
The point P(6,4) lies on the curve y = 4/(5 - x). (a) If Q is the point (x, 4/(5 - 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) 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 = X X X X (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(6,-4). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(6,-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(6,-4) lies on the curve y = 4/(5 - x).
(a) If Q is the point (x, 4/(5 - 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) 5.9
mpQ =
(ii) 5.99
mpQ
Need Help?
=
(iii) 5.999
mpQ =
(iv) 5.9999
mpQ
=
(v) 6.1
mpQ
=
(vi) 6.01
mpQ =
(vii) 6.001
mpQ=
(viii) 6.0001
mpQ=
X
X
Read It
X
(b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(6, -4).
m =
X
(c) Using the slope from part (b), find an equation of the tangent line to the curve at P(6, -4).
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