To find: The equation of the tangent line to the curve at the given point.
Answer to Problem 8E
The equation of the tangent line to the curve
Explanation of Solution
Given:
The equation of the curve is
The curve passing through the point (1, 1).
Formula used:
The slope of the tangent curve
The equation of the tangent line to the curve
Calculation:
Obtain the slope of the tangent line to the parabola at the point (1, 1).
Substitute
Since the limit x approaches 1 but not equal to 1, cancel the common term
Thus, the slope of the tangent line to the curve at the point (1, 1) is
Obtain the equation of the tangent line.
Since the tangent line to the curve
Substitute
Isolate y as shown below.
Thus, the equation of the tangent line is
Chapter 2 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning