Concept explainers
Tire graphs of f and g are given. Use them to evaluate each limit, if it exists. If the limit does not exist, explain why.
(a)
(b)
(c)
(d)
(e)
(f)
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Chapter 2 Solutions
EBK CALCULUS EARLY TRANSCENDENTALS
- Consider the function f(x) whose graph is shown below:arrow_forwardTopic : Limits of algebraic functionsarrow_forwardThe graph below is the function f(x) -2- -5 -4 -3 -2 2 -2 Determine the following values. Enter "DNE" if a value does not exist, enter "oo" (lower case "o") if the limit approaches positive infinity, or "-o0" if the limit approaches negative infinity. lim f(x) = lim f(x) = lim f(z) f(1)arrow_forward
- Let lim f(x) = 23 and lim g(x)= 7. Use the limit rules to find the following limit. X-8 X-8 lim [f(x) - g(x)] x-8 lim [f(x) - g(x)]= x-8 (Simplify your answer.)arrow_forwardPls help ASAParrow_forwardUse the graph of f in the figure to find the following values, if they exist. a. f(2) b. lim f(x) X→2 c. lim f(x) X→4 d. lim f(x) X→5 3- 0- 0 13 y = f(x) Xarrow_forward
- Use the graph of the function f shown below to respond to each prompt. The first prompt is worth 3 points. The other prompts are worth 0.5 points each: 10-9-8--6-5-4-3-2 ● Does Not Exist Undefined x→-3 lim x-3 . Can be found, lim f(x) lim x → 1 Does Not Exist Undefined f(x) = lim f(x) x →1 . Can be found, f(x) = The function has several discontinuities. State the location of two discontinuities and explain, using the definition of continuity, why the function is not continuous at that location. Does Not Exist Undefined f(- 6) 10+ 9 Edit Insert Formats B IU X₂ X² A E = = E- 3? e & N lim f(x) x+3+ . Can be found, lim f(x) = x+3+ 8+ f(-3) f(-7) . Can be found, f(-7)= . Can be found, f(-3) = Does Not Exist Undefined 7 6 5 4- 3 2 1 -2 -3 -4 -5 -6 -7 -8 9+ --10+ 2 A I V 4 5 6 7 8 9 10 Does Not Exist Undefined lim x →-3+ 。 Can be found, lim f(x) x → f(x) = - 3+ Does Not Exist Undefined f(1) Can be found, f(1) = Does Not Exist Undefined lim f(x) x →3 . Can be found, f(x) = lim x →3 Does Not…arrow_forward2. 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_forwardGive an example by sketching the graph of a function f that satisfies all the given conditions. lim (x--> -3) f(x)=+oo, lim (x--> -oo) f(x)=-2, f(0) = 0, f is even.arrow_forward
- The graph below is the function f(x) -5 -4 -3 -2 -1 3 2 1 lim f(x) = $2 f(2)= lim f(x) lim f(x) = 1 Determine the following values. Enter "DNE" if a value does not exist, enter "oo" (lower case "o") if the limit approaches positive infinity, or "-oo" if the limit approaches negative infinity. 200 2 3 4 Question Help: Message instructor D Post to forum Submit Question Q Searcharrow_forwardIf 3x-35 f(x)arrow_forwardIf 1 < f(x) < x² + 2x + 2 for all x, find lim f(x). X-1arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage