SubsequencesReal Analysis LabKaren DonnellyAll Rights ReservedLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2Iy1GLDYlUShyZXN0YXJ0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JUYrLUYjNiUtRiw2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUkobWZlbmNlZEdGJDYkLUYjNiMtRiw2JVEmcGxvdHNGJ0Y2RjlGQEYrRis=JSFHFor each of the sequences in exercise 19.3, page 188, find the set S of susequential limits, the limit superior, and the limit inferior.
<Text-field style="Heading 1" layout="Heading 1">Exercise 19a) The sequence <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1JJW1zdWJHRiQ2JS1GLDYmUSJzRicvJSVzaXplR1EjMjJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JS1GLDYmUSJuRidGN0Y6Rj1GNy9GPlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y3RkUvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRlAvJSlzdHJldGNoeUdGUC8lKnN5bW1ldHJpY0dGUC8lKGxhcmdlb3BHRlAvJS5tb3ZhYmxlbGltaXRzR0ZQLyUnYWNjZW50R0ZQLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGaW4tSSVtc3VwR0YkNiUtSShtZmVuY2VkR0YkNiUtRiM2Ji1GSzYuUSomdW1pbnVzMDtGJ0Y3RkVGTkZRRlNGVUZXRllGZW4vRmhuUSwwLjIyMjIyMjJlbUYnL0Zbb0Zoby1JI21uR0YkNiVRIjFGJ0Y3RkVGN0ZFRjdGRUZCLyUxc3VwZXJzY3JpcHRzaGlmdEdGSUY3RkVGK0Y3RkU=">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</Equation><Font size="22">. </Font></Text-field>Exercise 19a) The sequence LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JS1JJW1zdWJHRiQ2JS1GLDYlUSJzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiMtRiw2JVEibkYnRjdGOi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEiPUYnL0Y7USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGTS8lKXN0cmV0Y2h5R0ZNLyUqc3ltbWV0cmljR0ZNLyUobGFyZ2VvcEdGTS8lLm1vdmFibGVsaW1pdHNHRk0vJSdhY2NlbnRHRk0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0Zmbi1JJW1zdXBHRiQ2JS1JKG1mZW5jZWRHRiQ2JC1GIzYkLUZGNi1RKiZ1bWludXMwO0YnRklGS0ZORlBGUkZURlZGWC9GZW5RLDAuMjIyMjIyMmVtRicvRmhuRmVvLUkjbW5HRiQ2JFEiMUYnRklGSUY/LyUxc3VwZXJzY3JpcHRzaGlmdEdGREYr. Look at the first 25 terms of each of the sequences. LUkkc2VxRyUqcHJvdGVjdGVkRzYkKSEiIkkibkc2Ii9GKDsiIiIiI0Q=To plot this sequence we need to form the sequence of ordered pairs [n, 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] with the following command:Pkklc2VxYUc2IjcjLUkkc2VxRyUqcHJvdGVjdGVkRzYkNyRJIm5HRiQpISIiRisvRis7IiIiIiNEThen use the pointplot command to plot the sequence saved in seqa:LUkqcG9pbnRwbG90RzYiNiNJJXNlcWFHRiQ=From the above it is clear that this sequence diverges (since it oscillates between the values -1 and 1). LUkmbGltaXRHNiI2JCkhIiJJIm5HRiQvRihJKWluZmluaXR5RyUqcHJvdGVjdGVkRw==We can easily construct two subsequences of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYvNiVRIm5GJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==, one that converges to -1, and another that converges to 1, first by picking only terms with even subscripts, and second by picking only terms with odd subscripts. Pkkpc3Vic2VxYTFHNiI3Iy1JJHNlcUclKnByb3RlY3RlZEc2JDckLCRJIm5HRiQiIiMpISIiRisvRiw7IiIiIiNELUkqcG9pbnRwbG90RzYiNiNJKXN1YnNlcWExR0YkPkkpc3Vic2VxYTJHNiI3Iy1JJHNlcUclKnByb3RlY3RlZEc2JDckLCZJIm5HRiQiIiMiIiJGLikhIiJGKy9GLDtGLiIjRA==LUkqcG9pbnRwbG90RzYiNiNJKXN1YnNlcWEyR0YkJSFH
<Text-field style="Heading 1" layout="Heading 1">Exercise 19.3 b) </Text-field>Plot by combining two subsequencesPkkpc3Vic2VxYjFHNiI3Iy1JJHNlcUclKnByb3RlY3RlZEc2JDckLCZJIm5HRiQiIiMhIiIiIiItSSIvRzYkRihJKF9zeXNsaWJHRiQ2IywkRixGLS9GLDtGLyIjRA==QyQ+SSNwMUc2Ii1JKnBvaW50cGxvdEdGJTYkSSlzdWJzZXFiMUdGJS9JJmNvbG9yR0YlSSRyZWRHRiUiIiI=SSIlRzYiPkkpc3Vic2VxYjJHNiI3Iy1JJHNlcUclKnByb3RlY3RlZEc2JDckLCRJIm5HRiQiIiMqJCwmRixGLSEiIiIiIkYwL0YsO0YxIiNEQyQ+SSNwMkc2Ii1JKnBvaW50cGxvdEdGJTYkSSlzdWJzZXFiMkdGJS9JJmNvbG9yR0YlSSVibHVlR0YlIiIiSSIlRzYiLUkoZGlzcGxheUc2IjYjPCRJI3AxR0YkSSNwMkdGJA==
<Text-field style="Heading 1" layout="Heading 1">Exercise 19.3 (c) </Text-field> Look at the first 25 terms of each of the sequence:LUkkc2VxRyUqcHJvdGVjdGVkRzYkKiZJIm5HNiIiIiMsJiEiIiIiIilGK0YnRixGLC9GJztGLCIjRA==To plot this sequence we need to form the sequence of ordered pairs with the following command:Pkklc2VxY0c2IjcjLUkkc2VxRyUqcHJvdGVjdGVkRzYkNyRJIm5HRiQqJkYrIiIjLCYhIiIiIiIpRi9GK0YwRjAvRis7RjAiI0Q=Then use the pointplot command to plot the sequence saved in seqa:LUkqcG9pbnRwbG90RzYiNiRJJXNlcWNHRiQvSSZjb2xvckdGJEkkcmVkR0YkFrom the above it is clear that this sequence diverges (since it oscillates between the value 0 and values diverging to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JC1JI21vR0YkNi1RKiZ1bWludXMwO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZJLUYsNiVRKCZpbmZpbjtGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGKw==). LUkmbGltaXRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JComSSJuR0YnIiIjLCYhIiIiIiIpRi1GKkYuRi4vRipJKWluZmluaXR5R0YlAgain, we can easily construct two subsequences of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYvNiVRIm5GJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==, one that converges to 0, and another that diverges to infinity, first by picking only terms with even subscripts, and second by picking only terms with odd subscripts. Pkkpc3Vic2VxYzFHNiI3Iy1JJHNlcUclKnByb3RlY3RlZEc2JDckLCRJIm5HRiQiIiMqJi1JIl5HRig2JEYrRi0iIiIsJiEiIkYyKUY0RitGMkYyL0YsO0YyIiNELUkqcG9pbnRwbG90RzYiNiNJKXN1YnNlcWMxR0YkPkkpc3Vic2VxYzJHNiI3Iy1JJHNlcUclKnByb3RlY3RlZEc2JDckLCZJIm5HRiQiIiMhIiIiIiIqJkYrRi0sJkYuRi8pRi5GK0YvRi8vRiw7Ri8iI0Q=LUkqcG9pbnRwbG90RzYiNiNJKXN1YnNlcWMyR0Yk
<Text-field style="Heading 1" layout="Heading 1">Exercise 19.3 (d) </Text-field> Look at the first 25 terms of each of the sequence:LUkkc2VxRyUqcHJvdGVjdGVkRzYkKiZJIm5HNiIiIiItSSRzaW5HRig2IywkKiZGJ0YpSSNQaUdGJEYpI0YpIiIjRikvRic7RikiI0Q=To plot this sequence we need to form the sequence of ordered pairs [n, 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] with the following command:Pkklc2VxZEc2IjcjLUkkc2VxRyUqcHJvdGVjdGVkRzYkNyRJIm5HRiQqJkYrIiIiLUkkc2luRzYkRihJKF9zeXNsaWJHRiQ2IywkKiZGK0YtSSNQaUdGKEYtI0YtIiIjRi0vRis7Ri0iI0Q=Then use the pointplot command to plot the sequence saved in seqd:LUkqcG9pbnRwbG90RzYiNiRJJXNlcWRHRiQvSSZjb2xvckdGJEkkcmVkR0YkFrom the above it is clear that this sequence diverges (since it oscillates between the values 0, values going to -\342\210\236, and values going to -\342\210\236. LUkmbGltaXRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JComSSJuR0YnIiIiLUkkc2luR0YkNiMsJComRipGK0kjUGlHRiVGKyNGKyIiI0YrL0YqSSlpbmZpbml0eUdGJQ==We can easily construct three subsequences of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYvNiVRIm5GJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==, one that converges to 0, and another that diverges to\342\210\236 , and a third that diverges to -\342\210\236 -- 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSpwb2ludHBsb3RGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSlzdWJzZXFkM0YnRjRGNy9GOFEnbm9ybWFsRidGQkZCRisvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0ZC