3. The point P(2, – 1) lies on the curve y = 1/(1 - x). (a) If Q is the point (x, 1/(1 – x)), use your calculator to find the slope of the secant line PQ (correct to six decimal places) for the following values of x: (ii) 1.9 (vi) 2.1 (iii) 1.99 (vii) 2.01 (i) 1.5 (iv) 1.999 (v) 2.5 (viii) 2.001 (b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(2, – 1). (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(2, – 1).

3. The point P(2, – 1) lies on the curve y = 1/(1 - x). (a) If Q is the point (x, 1/(1 – x)), use your calculator to find the slope of the secant line PQ (correct to six decimal places) for the following values of x: (ii) 1.9 (vi) 2.1 (iii) 1.99 (vii) 2.01 (i) 1.5 (iv) 1.999 (v) 2.5 (viii) 2.001 (b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(2, – 1). (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(2, – 1).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

See similar textbooks