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 :
(i) 1.5
(ii) 1.9
(iii) 1.99
(iv) 1.999
(v) 2.5
(vi) 2.1
(vii) 2.01
(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).
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Student Solutions Manual for Stewart's Single Variable Calculus: Early Transcendentals, 8th (James Stewart Calculus)
Additional Math Textbook Solutions
Precalculus: A Unit Circle Approach
Precalculus: Mathematics for Calculus (Standalone Book)
University Calculus: Early Transcendentals (4th Edition)
Calculus Early Transcendentals, Binder Ready Version
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Calculus & Its Applications (14th Edition)
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning