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On [a,b], ARC = On [1, 16], find ARC for
![On [a,b], ARC = On [1, 16], find ARC for](http://images.slideplayer.com./27/9233295/slides/slide_1.jpg "On [a,b], ARC = On [1, 16], find ARC for")
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On [a,b], ARC = On [1, 16], find ARC for ARC = =
![On [a,b], ARC = On [1, 16], find ARC for ARC = =](http://images.slideplayer.com./27/9233295/slides/slide_2.jpg "On [a,b], ARC = On [1, 16], find ARC for ARC = =")
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On [a,b], ARC = On [1, 16], find ARC for ARC = =
![On [a,b], ARC = On [1, 16], find ARC for ARC = =](http://images.slideplayer.com./27/9233295/slides/slide_3.jpg "On [a,b], ARC = On [1, 16], find ARC for ARC = =")
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On [a,b], ARC = On [1, 16], find ARC for ARC = =
![On [a,b], ARC = On [1, 16], find ARC for ARC = =](http://images.slideplayer.com./27/9233295/slides/slide_4.jpg "On [a,b], ARC = On [1, 16], find ARC for ARC = =")
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Continuity This function is continuous on [0,3] Definition A function f is continuous at x = a means three things. 1) a is in the domain of f, 2)3)
![Continuity This function is continuous on [0,3] Definition A function f is continuous at x = a means three things.](http://images.slideplayer.com./27/9233295/slides/slide_5.jpg "1) a is in the domain of f, 2)3).")
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Continuity f is continuous on [0, 3] means that f is continuous at a for every a in [0, 3].
![Continuity f is continuous on [0, 3] means that f is continuous at a for every a in [0, 3].](http://images.slideplayer.com./27/9233295/slides/slide_6.jpg "Continuity f is continuous on [0, 3] means that f is continuous at a for every a in [0, 3].")
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Continuity f is continuous on [-1, 3) U (3, 4] means that f is continuous at x = a for every a in [-1, 3) U (3, 4].
![Continuity f is continuous on [-1, 3) U (3, 4] means that f is continuous at x = a for every a in [-1, 3) U (3, 4].](http://images.slideplayer.com./27/9233295/slides/slide_7.jpg "Continuity f is continuous on [-1, 3) U (3, 4] means that f is continuous at x = a for every a in [-1, 3) U (3, 4].")
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Continuity 1) a is in the domain of f, 2)3)
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Continuity Why wasn’t f continuous when x = 3? Must lift your pencil Not a valid reason
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Continuity 1) a is in the domain of f, 2)3) Why not at x = 3?
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Continuity 1) a is in the domain of f, 2)3) Yes on [-.2, 2) U (2, 3.1] Why not at x = 2?
![Continuity 1) a is in the domain of f, 2)3) Yes on [-.2, 2) U (2, 3.1] Why not at x = 2](http://images.slideplayer.com./27/9233295/slides/slide_11.jpg "Continuity 1) a is in the domain of f, 2)3) Yes on [-.2, 2) U (2, 3.1] Why not at x = 2")
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Continuity 1) a is in the domain of f, 2)3) Yes on [-.2, 2) U (2, 3.1] Why not at x = 2? Hole in the graph Not a valid reason
![Continuity 1) a is in the domain of f, 2)3) Yes on [-.2, 2) U (2, 3.1] Why not at x = 2.](http://images.slideplayer.com./27/9233295/slides/slide_12.jpg "Hole in the graph Not a valid reason.")
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Why is f not continuous at x = 1? A. 1 is not in the domain of f B.. C.. D. There is a hole in the graph E. Must lift your pencil
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Why is f not continuous at x = 1? A. 1 is not in the domain of f B.. C.. D. There is a hole in the graph E. Must lift your pencil
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f is continuous at x = 1. A. True B. False
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f is continuous at x = 1. A. True B. False
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f is continuous at x = 4. A. True B. False
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f is continuous at x = 4. A. True B. False
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Why is s continuous at 20? A. 20 is in the domain B.. C.. D. a, b, and c above E. none of the above
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Why is s continuous at 20? A. 20 is in the domain B.. C.. D. a, b, and c above E. none of the above
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f is continuous on [-2, 3]. A. Yes B. No
![f is continuous on [-2, 3]. A. Yes B. No](http://images.slideplayer.com./27/9233295/slides/slide_21.jpg "f is continuous on [-2, 3]. A. Yes B. No")
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f is continuous on [-2, 3]. A. Yes B. No
![f is continuous on [-2, 3]. A. Yes B. No](http://images.slideplayer.com./27/9233295/slides/slide_22.jpg "f is continuous on [-2, 3]. A. Yes B. No")
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Why is f not continuous at x=1? A. 1 is not in the domain B.. C.. D. All of the above
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Why is f not continuous at x=1? A. 1 is not in the domain B.. C.. D. All of the above
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Why is f not continuous at x=2? A. 2 is not in the domain B.. C.. D. All of the above
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Why is f not continuous at x=2? A. 2 is not in the domain B.. C.. D. All of the above
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Having thrown a pebble from the roof of MPP, will it pass the floor of the 3rd floor? Having thrown a pebble from the roof of MPP, will it pass the floor of the 3rd floor? The domain of this function is [a, b] representing the time it was thrown until the time the pebble struck the ground. The rule of the function, f, is "height of the pebble at time x". The domain of this function is [a, b] representing the time it was thrown until the time the pebble struck the ground. The rule of the function, f, is "height of the pebble at time x".
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Intermediate Value Theorem If f is continuous on [a, b] and d is inbetween f(a) and f(b), If f is continuous on [a, b] and d is inbetween f(a) and f(b), then c (a,b) such that f (c) = d. then c (a,b) such that f (c) = d.
![Intermediate Value Theorem If f is continuous on [a, b] and d is inbetween f(a) and f(b), If f is continuous on [a, b] and d is inbetween f(a) and f(b), then c (a,b) such that f (c) = d.](http://images.slideplayer.com./27/9233295/slides/slide_28.jpg "then c (a,b) such that f (c) = d..")
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f(x) = x 2 + x – 1.7 Prove f has a zero on [-1, 1] Prove f has a zero on [-1, 1] f(-1) = -1.7, f(1) = 0.3 f(-1) = -1.7, f(1) = 0.3 f is continuous on [-1, 1] f is continuous on [-1, 1] 0 (-1.7, 0.3) so by the IVT 0 (-1.7, 0.3) so by the IVT a c (-1, 1) so that f(c)= 0. a c (-1, 1) so that f(c)= 0.
![f(x) = x 2 + x – 1.7 Prove f has a zero on [-1, 1] Prove f has a zero on [-1, 1] f(-1) = -1.7, f(1) = 0.3 f(-1) = -1.7, f(1) = 0.3 f is continuous on [-1, 1] f is continuous on [-1, 1] 0 (-1.7, 0.3) so by the IVT 0 (-1.7, 0.3) so by the IVT a c (-1, 1) so that f(c)= 0.](http://images.slideplayer.com./27/9233295/slides/slide_29.jpg "a c (-1, 1) so that f(c)= 0..")
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Find c to make f continuous c/x must equal c/x must equal 4x + c 4x + c When x = 2 When x = 2 c/2 = 8 + c c/2 = 8 + c -8 = c/2 -8 = c/2 -16 = c -16 = c f(2) = -8 f(2) = -8
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Continuity This function is continuous on [0,3] d.n.e. d.n.e.Similarly, even though even though d.n.e. d.n.e.
![Continuity This function is continuous on [0,3] d.n.e.](http://images.slideplayer.com./27/9233295/slides/slide_31.jpg "d.n.e.Similarly, even though even though d.n.e. d.n.e..")
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