WRITING ABOUT CONCEPTS
Finding Functions Find
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EBK CALCULUS: EARLY TRANSCENDENTAL FUNC
- Finding Functions Find differentiable functions f and g that satisfy the specified condition such that lim f(x) = 0 and lim g(x) = 0. x→5 x→5 Explain how you obtained your answers. (Note: There are many correct answers.) f(x) f(x) (b) lim x→5 g(x) (a) lim 10 x→5 g(x) f(x) (c) lim x→5 g(x) = O0arrow_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_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
- Distance 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_forwardlim 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
- 3. 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@Test the analyticity 2 . f(z) = z² @ f(Z) = (Z)" of the following functions. • f(z) = ² fiz) = 32² +52-61arrow_forwardProof Prove that if lim f(x) = 0, then lim f(x)| = 0.arrow_forward
- f(x) 4) Let lim f(x) = 7, and lim g(x) = 6. Find lim 3 X-5 X-5 x-5 g(x)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_forwardDescription lim f(x) Find where J is the function defined by 1-x if x 0 x+2arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning