Concept explainers
The graph of f is given,
(a) Find each limit, or explain why it does not exist.
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(b) State the equations of the vertical asymptotes.
(c) At what numbers if f discontinuous? Explain.
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Chapter 1 Solutions
Calculus (MindTap Course List)
- Find limx2x24x2.arrow_forwardUse the given graph of f to state the value of each quantity, if it exists. If it does not exist, explain why. (a) lim f(x) (b) lim f(x) x→2+ (c) lim f(x) x→2- (d) f(2) (e) lim f(x) (f) f(4) x→4 YA 4- 201olqurv leinv Sdi bni 2- means h in Figu 14. 4arrow_forwardFor the function f whose graph is given, state the value of each quantity, if it exists. If it does not exist, explain why. (a) lim f(x) (b) lim f(x) (c) lim f(x) エ→1- (d) lim f(x) (e) f(3) -2 2 4arrow_forward
- For the function h whose graph Is glven, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.) yA A 4 -4 -2 4 (a) lim h(x) 4 (ь) lim h(x) x- -3 lim h(x) --3 (c) (d) h(-3) 3 (e) lim h(x) x- 0 1 (f) lim h(x) o+ -1 (g) lim h(x) XTO (h) h(0) (i) lim h(x) x - 2 () h(2) (k) lim h(x) x- 5* (1) lim h(x)arrow_forwardUse 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_forwardSketch the graph of an example of a function f that satisfies lim f(x) 210 = 1arrow_forward
- The graph below is the function f(x) 4- -5 -4 -3 -2 -1 1 2 3 4 -2 -3 -4 -5 Find lim f(æ) x →2- Find lim x →2+ f(x) Find lim f(x) x → 2 Find f(2) 3.arrow_forwardUse the given graph of f to state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.) YA -2 2 4 lim f(x) (a) X → 2- (Б) lim f(x) X → 2+ (c) lim f(x) X → 2 (d) f(2) e) lim f(x) X → 4 (f) f(4) 4.arrow_forwardUse the given graph of f to state the value of each quantity, if it exists. (If it does not exist, enter NONE.) y 10 8 4 -2 2 4 (a) lim f(x) x-1 (b) lim f(x) x-1 (c) lim f(x) x-1 (d) lim_f(x) X-5 (e) f(5)arrow_forward
- For the function whose graph is given, state the value of each quantity, if it exists. If it does not exist, explain why. (a) lim g(t) (b) lim g(t) (c) lim g(t) 2 (d) lim g(t) (e) lim g(t) (f) lim g(t) -2- (g) g(2) (h) lim g(t) 2arrow_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_forwardFor the function f whose graph is given below, state the value of each quantity, if it exists. y 5t 3 2 2 (a) lim f(x) = X- 2 lim f(x) = x+2+ (b) %3D (c) lim f(x) : x-2 (d) lim f(x) = x-1 (e) f(1) = %3D 후arrow_forward
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