Concept explainers
Continuity and limits with transcendental functions Determine the interval(s) on which the following functions are continuous; then analyze the given limits.
51.
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
Precalculus
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
- using 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_forwardUse analytical method to determine if the limit of a function g(x) as x approaches - 2 exists. Explain the answer and the procedures you applied briefly.arrow_forwardH(3)=6 and the limit as x approaches 3 of H(x) is 6. Mustache be continuous at (3,6)? State why.arrow_forward
- Use L' Hopital's to find the limit as x approaches positive infinity of: (e^(3x))/(x^(2)) I hope you have a nice day!arrow_forwardlimit of (x + 5) as x approaches to 3 po yung given if ever blurred. ty!arrow_forwardConsider the function g(x) = cos(1/x). We will investigate the limit behavior at x = 0. c) If n is an arbitrary positive integer, find points x1 and x2 (int terms of n) in the interval(-1/n, 1/n( such that g(x2) = 1 and g(x2) = -1. d) Explain (in a brief paragraph) why (c) implies that g does not have a limit at x = 0. e) Where is g continuous? Justify your answer. You may use facts from the textbook in Section 2.2 - 2.5.arrow_forward
- limit of x to infinity Square root(x^2-2x+1)-xarrow_forwardLet f(x)= 2x-2 if x<1 f(x)=x^2-1 if x is greater than or equal to 1 Evaluate Lim h-->0+ f(1+h)-f(1)/h Evaluate Lim h-->0- f(1+h)-f(1)/h Is the function f differentiable at a=1? Justify your answer.arrow_forwardlimit as x approaches infinity of (e^x + e^-x)/(e^x - e^-x)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage