Concept explainers
Evaluating a Limit In Exercises 43-62, (a) describe the type of indeterminate form (if any) that is obtained by direct substitution. (b) Evaluate the limit, using L’Hôpital’s Rule if necessary. (c) Use a graphing utility to graph the function and verify the result in part (b).
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Calculus of a Single Variable
Additional Math Textbook Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Calculus: Early Transcendentals (2nd Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
Precalculus: Mathematics for Calculus - 6th Edition
Precalculus: Mathematics for Calculus (Standalone Book)
Calculus: Early Transcendentals (3rd Edition)
- Limit and Continuity In Exercises , find the limit (if it exists) and discuss the continuity of the function. 14. lim (x, y)→(1, 1) (xy) /(x^2 − y^2 ) 16. lim (x, y)→(0, 0) (x^2 y) /(x^4 + y^2)arrow_forward(Right and Left Limits). Introductory calculus coursestypically refer to the right-hand limit of a function as the limit obtained by“letting x approach a from the right-hand side.” (a) Give a proper definition in the style of Definition 4.2.1 ((Functional Limit).for the right-hand and left-hand limit statements: limx→a+f(x) = L and limx→a−f(x) = M. (b) Prove that limx→a f(x) = L if and only if both the right and left-handlimits equal L.arrow_forwardShowing a Limit Does Not Exist Examine lim --- numerically. Then prove that the limit does not exist.arrow_forward
- Consider the limit. (a) Describe the type of indeterminate form that is obtained by direct substitution. (b) Evaluate the limit. Use a graphing utility to verify the result.arrow_forwardproof of The Cancellation Theorem for Limitsarrow_forwardFinding the Derivative by the LimitProcess In Exercises 15–28, find the derivativeof the function by the limit process f (x) = 7x − 3arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning