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1 Continuit, End Behavior, and Limits Assignment Determine whether each function is continuous at the given -values. Justif using the continuit test. If discontinuous, identif the tpe of discontinuit as infinite, jump, or removable.. f = + at =. 7 f = if > 0 if < 0 = Copright PreCalculusCoach.com
2 Continuit, End Behavior, and Limits Assignment. f = + if 0 if < 0 at = 0. f = + at = Copright PreCalculusCoach.com
3 Continuit, End Behavior, and Limits Assignment. f = + at = and =. f = + at = and = Copright PreCalculusCoach.com
4 Continuit, End Behavior, and Limits Assignment Find the value of k so that f is continuous. 7. f = k + if > + k if. f = + if > 0 k if = 0 + if < 0 Determine between which consecutive integers the real zeros of function are located on the given interval. 9. f = + [0, ] 0. f = [, ] Copright PreCalculusCoach.com
5 Continuit, End Behavior, and Limits Assignment Use the graph of each function to describe its end behavior. Support the conjecture numericall.. f = f = + 0 Evaluate the following limits lim = =?. lim =? Copright PreCalculusCoach.com
6 Continuit, End Behavior, and Limits Assignment Determine the interval(s) on which the function is increasing and the interval(s) on which the function is decreasing.. f = f = Copright PreCalculusCoach.com
7 Continuit, End Behavior, and Limits Assignment ANSWERS Determine whether each function is continuous at the given -values. Justif using the continuit test. If discontinuous, identif the tpe of discontinuit as infinite, jump, or removable.. f = + at =. 7 f = if > 0 if < 0 = f = + at = f = + f = f eists F f I f = if > 0 if < 0 f is undefined in = 0 if > 0 f = if < 0 is discontinuous at = 0 0 F 0 = f f I f = and from both side of = lim + = f () f = + is continuous at = f if > 0 f = has point discontinuit if < 0 since 0 on opposite sides of = 0 = 0 is point of Copright PreCalculusCoach.com 7
8 Continuit, End Behavior, and Limits Assignment. f = + if 0 if < 0 at = 0. f = + at = f = + if 0 if < 0 f 0 = + = 0 + = f 0 eists at = 0 f = + at = f = + f = 7 f eists 0 F 0 F 7 0 I f f I f f = f f has jump discontinuit at = 0 and 7 from both side of = lim + = f () f = + is continuous at = Copright PreCalculusCoach.com
9 Continuit, End Behavior, and Limits Assignment. f = + at = and =. f = + at = and = 0 + f = at = and = + f = = f = = 0 f and f are undefined F f I f lim f() 0. F F I f f 0 00, 000 lim f() does not eists lim f() 0. but f is undefined F f has a removable discontinuit at = f has an infinite discontinuit at = f = + f = + f = + at = and = = 0 0 = 0 0 = 0 f undefined F f I f lim f() = 0 F F I lim F f f lim f() = f = 0 f() eists but f is undefined f has a removable discontinuit at = lim f() = f = 0 f is continuous at = Copright PreCalculusCoach.com 9
10 Continuit, End Behavior, and Limits Assignment Find the value of k so that f is continuous. 7. f = k + if > + k if k + = + k =. f = + if > 0 k if = 0 + if < 0 + = + = 0 k + = + k k + = + k 9k = k = = + = k = Determine between which consecutive integers the real zeros of function are located on the given interval. 9. f = + [0, ] 0. f = [, ] f is negative positive and f is positive, f change sign in f has zero in interval: 0 7 f is negative and f is positive, f change sign in f is positive and f is negative f change sign in f has zeros in intervals: and Copright PreCalculusCoach.com 0
11 Continuit, End Behavior, and Limits Assignment Use the graph of each function to describe its end behavior. Support the conjecture numericall.. f = From the graph, it appears that: f as and f as The table supports this conjecture f = From the graph, it appears that: f as and f as The table supports this conjecture Evaluate the following limits.. lim = =?. lim =? Copright PreCalculusCoach.com
12 Continuit, End Behavior, and Limits Assignment lim = + = lim = lim ( + ) = + = lim + = lim = lim = lim = Determine the interval(s) on which the function is increasing and the interval(s) on which the function is decreasing.. f = From the graph, it appears that: A function + + is increasing for < 0. A function + + is decreasing for > 0. The table supports this conjecture f = From the graph, it appears that: A function + 9 is increasing for <. A function + 9 is decreasing for. < < 0. A function + 9 s increasing for > 0. The table supports this conjecture Copright PreCalculusCoach.com
13 Continuit, End Behavior, and Limits Assignment Copright PreCalculusCoach.com
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