Concept explainers
In Exercises 1–4, use the given table of values to estimate, for the given value of a, each of the following if they exist:
(a)
(b)
(c)
(d)
[HINT: See Example 1-3]
|
–0.1 | –0.01 | –1.001 | –0.0001 | 0 | 0.0001 | 0.001 | 0.01 | 0.1 |
|
–1.0303 | –1.00303 | –1.0003 | –1.00003 | 0 | 1.00003 | 1.0003 | 1.00303 | 1.0303 |
Trending nowThis is a popular solution!
Chapter 3 Solutions
Applied Calculus
Additional Math Textbook Solutions
Precalculus Enhanced with Graphing Utilities (7th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Calculus and Its Applications (11th Edition)
Precalculus: A Unit Circle Approach (3rd Edition)
- (b) If we keep the first part of the hypothesis of Theorem 5.3.6(L’Hospital’s Rule) the same but we assume that lim f'(x)/g'(x) = ∞, x→a does it necessarily follow that lim f(x)/g(x)= ∞?, x→aarrow_forwardIn Exercises 27–32, use a graphingutility to graph the function on the closed interval [a, b].Determine whether Rolle’s Theorem can be applied to f on theinterval and, if so, find all values of c in the open interval (a, b)such that f '(c= ' 0.) f(x)=|x|-1,[-1,1]arrow_forwardEvaluate the limit. lim e2/(x-3)x →3-arrow_forward
- suppose f,g an d h are functions which g(x)<=f(x) <=h(x) ,for all x in an open interval containing a , except possibly at a. if lim g(x) ,x approaches to a does not exist or lim h(x) ,x approaches to a does not exist , will the lim f(x) ,x approaches to a do or does not exist ?arrow_forwardLet F(x) = (x2 + 3x + 2)/(2 - | x | ). Make tables of values of F at values of x that approach c = -2 from above and below. Then estimate limx→ -2 F(x).arrow_forward1. Using tables of values, estimate lim 3x x→2 a. 3 b. 6 c. 2 d. 5 2. Using tables of values, estimate lim (x2+4x−3) x→1 a. 1 b. 3 c. 0 d. 2 3. Using tables of values, estimate lim (x3−2x2−3) and lim (x3−2x2−3) x→2- x→2+ a. -19 and -3, respectively b. -3 and -19, respectively c. both equal to -3 d. both equal to -19arrow_forward
- Find the constant c so that the limit limx->3 (x2+x+c)/(x2-5x+6) exists.arrow_forwardProve that lim x approaches c .......... ƒ(x) = L if and only if lim hS0 ƒ(h + c) = L.arrow_forwardIs there a value of a for which limx1 3x^2+ax+a+3/x^2+x-2 exists? Enter the value of a if such a exist otherwise enter 0.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