Concept explainers
Evaluating Limits In Exercises 37-40, use the information to evaluate the limits.
(a)
(b)
(c)
(d)
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Bundle: Calculus: Early Transcendental Functions, 7th + Webassign, Multi-term Printed Access Card
- zle: BCT5-8 Jse the graph to determine the following limits. (a) lim f(x) (b) lim f(x) Xー (c) lim f(x) Xー→3 (d) lim f(x) ズー→4 Use the graph to determine the following limits. y=f(x) 2- (a) lim f(x) (b) lim f(x) x→2 (c) lim f(x) (d) lim f(x) x-3 xー→4 -1+arrow_forwardReal analysisarrow_forwardQuestion: What does the graph of f(x) say about the value of lim f(x)? x->-1+ y -3 -2 2 3arrow_forward
- 2. A portion of the graph of the function y = f(x) is shown in the figure. (a) State the domain and range of f. (b) Find the values: f(-2) and f(3). (c) Use the graph to determine each of the limits: (i) lim f(x); lim f(x); lim f(x) x-2+ x-2- x-2 (ii) lim f(x); lim f(x); x-3 lim f(x). x+3 3. The graph of the function y = k(x) is shown in the figure. (a) Write a piecewise formula for the function k. (b) Evaluate the one-sided limits of k at x = 1 algebraically, by using your formula from part (a). y=f(x) 1+ fif 1 -1- 2 1.5 1 4. Let f(x) = |x| and g(x) = x - 3. (a) Determine the formulas for each of the related composite functions: h(x) = (fog)(x) = f(g(x)) s(x) = (gof)(x) = g(f(x)) t(x) = (gofᵒg)(x) = g(f(g(x))). 5. (a) Find the values of x₁ and x₂ in the figure. (b) Find the largest positive number 8 such that: |-1|<0.1 whenever 0<|x-1|<8. Hint: Choose to be the minimum value of |x-1| for i = 1,2. (b) Plot graphs of all the functions: f,h, s, and t in the same coordinate plane. Use…arrow_forwarda) Determine whether the statement is true or false. Explain your answer. (3 rs2 If f(x)= then lim f (x) = 3 0 x>2 True False b) Find two functions f and g such that lim f (x) and lim f (x) do not exist, but lim[f(x)+ g(x)]does exist.arrow_forwardThe graph below is the function f(x) 25+ 20 15 10 10 15 20 25 25 -20 -15 -10 -5 -5 -10 -15 -20 -25 lim f(x) = f(- 5) = 5.arrow_forward
- Sketch the graph of an example of a function f that satisfies all of the given conditions. lim f(x) = 4, f(5) = 5, f(-1) = 3 lim f(x) = 6, X-5+ lim f(x) = 4, X-5- y x 1 O -5 -5 6 2 6 2 5 -5 y 6 2 5 x y 2 6 x 5 -5 2 5 xarrow_forwardPostage The graph below shows how the postage required to mail a letter in the United States has changed in recent years. Let C(t) be the cost to mail a letter in the year t. Find the fol- lowing. Source: United States Postal Service. lim C(1) (a) 2014 (c) lim C(t) (b) lim C(t) 2014* (d) C(2014) -2014 C(t) 50 40 30 *02 ++ *06 80. *12 *14 of +++++ *13 L0. Year 2001 60. Cost (in cents)arrow_forwardSolve A, B, & C.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