The point P(3, -3) lies on the curve y = 3/(2 – x). ASK YOUR (a) If Q is the point (x, 3/(2 - 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) 2.9 MPQ = 3.33 (ii) 2.99 mPQ = 3.0303 (iii) 2.999 mPQ = 3.003003 (iv) 2.9999 mpo = 3.003003 (v) 3.1 mPo = 2.722222 (vi) 3.01 mpo = 2.9702 (vii) 3.001 mpo = 2.997002 (viii) 3.0001 mpg - 2.999700 (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(3, -3). m- 3 (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(3, -3). y = 3x

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(3, –3) lies on the curve y = 3/(2 – x).
ASK YOUR
(a) If Q is the point (x, 3/(2 – 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) 2.9
MPQ = 3.33
(ii) 2.99
mPQ = 3.0303
(iii) 2.999
mPQ = 3.003003
(iv)
2.9999
mpo = 3.003003
(v) 3.1
mPo = 2.722222
(vi) 3.01
mpo = 2.9702
(vii) 3.001
mpo = 2.997002
(viii)
3.0001
mpo - 2.999700
(b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(3, -3).
m 3
(c) Using the slope from part (b), find an equation of the tangent line to the curve at P(3, -3).
y = 3x
Transcribed Image Text:The point P(3, –3) lies on the curve y = 3/(2 – x). ASK YOUR (a) If Q is the point (x, 3/(2 – 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) 2.9 MPQ = 3.33 (ii) 2.99 mPQ = 3.0303 (iii) 2.999 mPQ = 3.003003 (iv) 2.9999 mpo = 3.003003 (v) 3.1 mPo = 2.722222 (vi) 3.01 mpo = 2.9702 (vii) 3.001 mpo = 2.997002 (viii) 3.0001 mpo - 2.999700 (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(3, -3). m 3 (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(3, -3). y = 3x
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