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Finding Functions Find
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Chapter 8 Solutions
Calculus: Early Transcendental Functions
- using the definition find f(x)arrow_forwardDistance A line with slope m passes through the point (0, – 2). (a) Write the distance d between the line and the point (4, 2) as a function of m. (Hint: See Section P.2, Exercise 77.) (b) Use a graphing utility to graph the equation in part (a). (c) Find lim d(m) and lim d(m). Interpret the results geometrically.arrow_forwardDistance A line with slope m passes through the point (0, 4). (a) Write the distance d between the line and the point (3, 1) as a function of m. (Hint: See Section P.2, Exercise 77.) (b) Use a graphing utility to graph the equation in part (a). (c) Find lim d(m) and lim d(m). Interpret the results m→-00 geometrically.arrow_forward
- Tutorial 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_forwardf(x) 4) Let lim f(x) = 7, and lim g(x) = 6. Find lim 3 X-5 X-5 x-5 g(x)arrow_forward3. Let f(x) =-2x2 + 4x-5. Use the limit definition of the derivative (or the four-step process) to find f'(x). ' ISe thea cection 91 h: use thearrow_forward
- lim f (x) Determine f(x) 6 (3,4) 0.3). (3, 2) (-2, 1); (3,0) -3 -1 4arrow_forwardUse the graph of the function f to decide whether each quantity exists. (If an answer does not exist, enter DNE.) 10 2 4 6 8 10arrow_forward@Test the analyticity 2 . f(z) = z² @ f(Z) = (Z)" of the following functions. • f(z) = ² fiz) = 32² +52-61arrow_forward
- Proof Prove that if lim f(x) = 0, then lim f(x)| = 0.arrow_forwardLearning Task 7: Sketch one possible graph of a function f(x) defined on R that satisfies all the listed conditions. You can use different colors of pen and high- KAS light the hole and point on the graph lim f(x) = DNE lim f(x) = 0 lim f(x) = 0 ズ→ー1 lim f(x) = 2 x-4 lim f(x) = DNE lim f(x) = -3 lim f(x) = 5 lim f(x) = 5 c>4 x+1 ズ→4 Tasks: 1. Sketch one possible graph that satisfies the condition 2. Design your graph. 3. Explain your work or solutions why did you arrive with that kind of graph. (Please use an oslo paper in doing this learning task.) Scoring Rubric Category Еxcellent Satisfactory Very Satisfactory Needs Improvement Content- Ac- 100% of the solu- 80 -99% of the 60-79% of the Below 60% of curacy (20) tions are correct. solutions are solutions are the solutions (20) correct (17) correct (14) are correct (11) Output is dis- tractingly Presentation Output is at- Output is ac- ceptably attrac- tive though it may be a bit Output is excep- tionally attractive of Output tractive…arrow_forwardQuestion Select your answer. If f(x) = { 9(x), ifr 2 where g and h are polynomial Yes, because lim f(x) = f(2). functions with distinct values at z = 2, can f(x) be continuous at r = 2? Why? No, because lim f(x) + f(2). Yes, because g(2) and h(2) are both defined. No, because f(2) is not defined and lim f(x) exists. Answerarrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
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