Concept explainers
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.
8.
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
Single Variable Calculus
- 1. 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_forward1. Using the table of values, estimate lim 3x x→2 a. 3 b. 6 c. 2 d. 5 2. Using the table of values, estimate lim (x2 + 4x -3) x→1 a. 1 b. 3 c. 0 d. 2 3. Using the table 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_forwardUsing the definition to show both limits: limx→±∞x^2/x^2+4 =1arrow_forward
- Cal L'hospital rule be used when evaluating the lim as x approaches infinity is e4x-x2/ex(x3+x) or lim as x approaches 1 is n(x) / exarrow_forwardFind the value of lim x→0 8sin2x/ 7sin(2x^2+x).arrow_forwardGiven limx→3f(x) = 5, limx→3g(x) = −2, and limx→3h(x)= −3, find the following limits a. limx→3[ 3f(x) + 5h(x)] b. lim??→3[5f(x)∙g(x)/h(x) ] c. limx→3 sq root −3/ h(x) +10/f(x) -3g(x)arrow_forward
- 1) Explain what it means to say that lim x → 4− f(x) = 3 and lim x → 4+ f(x) = 1. A)As x approaches 4 from the right, f(x) approaches 3. As x approaches 4 from the left, f(x) approaches 1. B)As x approaches 4 from the left, f(x) approaches 3. As x approaches 4 from the right, f(x) approaches 1. C)As x approaches 4, f(x) approaches 1, but f(4) = 3. D)As x approaches 4, f(x) approaches 3, but f(4) = 1. In this situation is it possible that lim x → 4 f(x) exists? Explain. A)Yes, f(x) could have a hole at (4, 3) and be defined such that f(4) = 1. B)Yes, f(x) could have a hole at (4, 1) and be defined such that f(4) = 3. C)Yes, if f(x) has a vertical asymptote at x = 4, it can be defined such that lim x→4− f(x) = 3, lim x→4+ f(x) = 1, and lim x→4 f(x) exists. D)No, lim x→4 f(x) cannot exist if lim x→4− f(x) ≠ lim x→4+ f(x).arrow_forwardcompute the indicarted limit. write your answer in fraction, if necessary lim as x approaches 2 of x^2-3x+2 divided by x^2-x-2arrow_forward1. a) Which limit requires algebraic simplification? Circle your answer. i) lim x→6 6−√x / x−36 ii) lim x→36 6−√x/ x−36 b) Explain the process you would take to simplify.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