Concept explainers
Continuity of functions with absolute values Use the continuity of the absolute value function (Exercise 66) to determine the interval(s) on which the following functions are continuous.
69.
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Calculus: Early Transcendentals, Books a la Carte Plus MyLab Math/MyLab Statistics Student Access Kit (2nd Edition)
Additional Math Textbook Solutions
Calculus & Its Applications (14th Edition)
Glencoe Math Accelerated, Student Edition
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus and Its Applications (11th Edition)
- f(x)={(4-2x, x<=2), (x^(2)-3, x>2)} Describe the interval(s) on which the function is continuous. (Interval Notation) What discontinuities are not satisfied?arrow_forward116. Proof Use the definitions of increasing and decreasing functions to prove that $f(x)=x^{3}$ is increasing on $(-\infty, \infty)$.arrow_forwardContinuity of a piecewise function Let For what values of a is ƒ continuous?arrow_forward
- First Derivative Testa. Locate the critical points of f.b. Use the First Derivative Test to locate the local maximum andminimum values.c. Identify the absolute maximum and minimum values of the functionon the given interval (when they exist).arrow_forwardDiscontinuous composite of continuous functions Give an example of functions ƒ and g, both continuous at x = 0, for which the composite ƒ g is discontinuous at x = 0.arrow_forwardusing the definition of continuity and the properties of limits to show that the function is continuous at the given number a. f(x)= 3x2+(x+2)5, a= -1 can you please explain this problem with workarrow_forward
- Use closed interval method to find the absolute max and min values of f(x)= x/(x^2 +2) on the interval -1 less than or equal to x less than or equal to 4. Show work using calculus and round to 2 decimal places if neededarrow_forwardFind all numbers c that satisfy the conclusion of Rolle's Theorem for the following function and interval. Enter the values in increasing order and enter N in any blanks you don't need to use. f(x)=4x * sq.rt. (x+10) , [-10,0]. _ ,_ ,_ ,_ ?arrow_forward15 determine if the function is continuous or not. type continuous if the function is continuous at a certain value of x. if the answer is dicontinuous, determine what type of discontinuity (removable discontinuity, jump discontinuity, infinite dicontinuity) SHOW SOLUTIONarrow_forward
- Using analytical methods, find all critical numbers (exact values) of the function.f(x) = 1/(x − 1)^2 −1/x^2arrow_forwardUsing the First Derivative Test Consider the function ƒ(x) = 3x4 - 4x3 - 6x2 + 12x + 1.a. Find the intervals on which ƒ is increasing and those on which it is decreasing.b. Identify the local extrema of ƒ.arrow_forwardContinuity Determine the interval(s) on which the following functions are continuous.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