Concept explainers
Miscellaneous limits Use the method of your choice to evaluate the following limits.
61.
Want to see the full answer?
Check out a sample textbook solutionChapter 15 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Thomas' Calculus: Early Transcendentals (14th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Glencoe Math Accelerated, Student Edition
University Calculus: Early Transcendentals (4th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
- The continuous extension of (sin x)^x [0,π] a) Graph f(x)= (sin x)^x on the interval 0 ≤ x ≤ π. What value would you assign to f(x) to make it continuous at x = 0? b) Verify your conclusion in part (a) by finding limx→0+ f(x) with L’Hôpital’s Rule. c) Returning to the graph, estimate the maximum value of f(x) on [0, π].About where is max f(x) taken on? d) Sharpen your estimate in part (c) by graphing ƒ in the same window to see where its graph crosses the x-axis. To simplify your work, you might want to delete the exponential factor from the expression for f' and graph just the factor that has a zero.arrow_forwardLet f(x, y) = x/(y − 1)^2 . a. Describe the domain of f. b. Sketch the level curves of f corresponding to the values −1, 0 and 1. Explain how you know what the level curves look like. c. Show that the limit lim (x,y)→(0,1) f(x, y) does not exist.arrow_forwardLIM x to 09 tanh(x)/tan(x) using the L'hospital's rulearrow_forward
- lim(x,y) aproaches (0,0) (3x3y)/(x6+y2)arrow_forwardThe continuous extension of (sin x)x [0, Pi]a) Graph f(x)= (sinx)x on the interval 0 ≤ x ≤ Pi. What value would youassign to f(x) to make it continuous at x = 0?b) Verify your conclusion in part (a) by finding lim ?→0+ ?(?) with L’Hôpital’s Rule.arrow_forwardnd the limit, if it exists. If the limit does not exist, explain why. limx→2 1−|x|^2/1−x^2 You must show ALL of your work in order to receive full credit. Do NOT use differentiation. Do NOT use L'Hospital's Rule.arrow_forward
- Guess the value of the limit (if it exists) by evaluating the function at the given numbers. (It is suggested that you report answers accurate to at least six decimal places.) Let f(x)= cos(9x)−cos(10x)/x2 We want to find the limit limx→0 cos(9x)−cos(10x)/x2Start by calculating the values of the function for the inputs listed in this table. x x f(x)f(x) 0.2 0.1 0.05 0.01 0.001 0.0001 0.00001 Based on the values in this table, it appears limx→0 cos(9x)−cos(10x)/x2=?arrow_forwardGuess the value of the limit (if it exists) by evaluating the function at the given numbers. (It is suggested that you report answers accurate to at least six decimal places.) Let f(x)=cos(9x)-cos(5x)/x2 We want to find the limit limx→0 cos(9x)−cos(5x)/x2Start by calculating the values of the function for the inputs listed in this table. x x f(x)f(x) 0.2 0.1 0.05 0.01 0.001 0.0001 0.00001 Based on the values in this table, it appears limx→0 cos(9x)−cos(5x)/ x2arrow_forwardUsing l’Hôpital’s Rule Evaluate the following limits.arrow_forward
- 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