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Asymptotes of a function containing exponentials Let
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Chapter 2 Solutions
Calculus: Early Transcendentals (2nd Edition)
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- question in the picturearrow_forward2. Reviewing the functions f(x) = e and g(x) = ln x. (a) Neatly graph f(x) = e, g(x) = lnx and h(x) = x on the same set of axes. Make sure to label their x- and y-intercepts and the asymptotes too (if they exist). What is the domain of f? What is the range of f? What is the domain of g? What is the range of g? What is the domain of h? What is the range of h? (b) Find f(g(x)) and g(f(x)). Simplify. Are f and g inverse functions? How can you tell?arrow_forwardTutorial Exercise Use the given graph of the function y = f(x) to find the following quantities, if they exist. y 3 1 -6 -5 -4 -3 -2 -1 1 (a) lim f(x) X-4 (b) lim f(x) X-1- (c) x--1+ lim f(x) (d) lim f(x) x--1 (e) f(-1) Step 1 of 3 (a) lim f(x) X→-4 Recall lim f(x) exists if and only if lim f(x) = lim f(x). a+ Xa Xa Also recall lim f(x) = L if the values of f(x) can be made arbitrarily close to L by taking x sufficiently close to a for Xa x a. Using the graph, find the values (if they exist) of lim f(x) and lim f(x). (If a limit does not exist, enter DNE.) X→-4+ X-4- lim f(x) = X→-4- lim f(x) = X→-4+ O, lim f(x) ---Select--- X--4 O and its value is as follows. (If the limit does not Since these limits -Select--- exist, enter DNE.) lim f(x) = X-4arrow_forward
- Find the vertical asymptotes (if any) of the graph of the function f(x) = csc xarrow_forwarde2h-1 if f'(a) lim-0 what is f(r) and what is a? harrow_forwarde-3x – In(x + 1) if x 0 5x (a) Evaluate lim f(x). Show work (calculation steps or a written explanation) in order to receive full credit. (b) ; Is the function continuous at a = 0? Explain why or why not.arrow_forward
- Sketch a graph of a function f(x) that has the following properties: lim as x approaches -infinity is f(x)= infinity lim as x approaches -6 from the left is f(x) infinity and lim as x approaches -6 from the right is f(x)= -infinity lim as x approaches -3 is f(x)= -5 f(-3)=6 f(0)=1 f'(0)=0 f''<0 on the interval (-3,0) f''>0 on the interval (0, infinity) f'> 0 on the interval (0,infinity)arrow_forwardThe figure shows the graph of f(x) = ln x. Use transformations of this graph to graph the function h(x) = -ln x. Graph and give equations of the asymptotes. Use the graphs to determine the function’s domain and range.arrow_forwardCalculus - (Show all work, no calculator)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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