This lab shows how to create finite sequences or lists when you put [] around the sequence. We will use these sequences to give an idea of what a limit is, how we get derivatives and to prove the fundamental theorem of calculus that allows us to use antidifferentiation to evaluate definite integrals. Later on we will see how we deal with infinite sequences and series and representations of functions by an infinite series. Don't forget to hit the !!! to redo all of the outputs here so that you get what you expect.restart;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYmLUYjNiQtSSNtaUdGJDYlUSRzZXFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiw2JC1GIzYpLUYxNiVRIm5GJ0Y0RjctSSNtb0dGJDYtUSIsRicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y2LyUpc3RyZXRjaHlHRkkvJSpzeW1tZXRyaWNHRkkvJShsYXJnZW9wR0ZJLyUubW92YWJsZWxpbWl0c0dGSS8lJ2FjY2VudEdGSS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnRj4tRkI2LVEiPUYnRkVGRy9GS0ZJRkxGTkZQRlJGVC9GV1EsMC4yNzc3Nzc4ZW1GJy9GWkZbby1JI21uR0YkNiRRIjFGJ0ZFLUZCNi1RIy4uRidGRUZHRmluRkxGTkZQRlJGVC9GV1EsMC4yMjIyMjIyZW1GJy9GWkZYLUZebzYkUSQxMDBGJ0ZFRkVGRS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJy1GQjYtUSI7RidGRUZHRkpGTEZORlBGUkZURlZGXG8=print(); # input 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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVElcGxvdEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIihGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdRJmZhbHNlRicvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdGTC8lK2V4ZWN1dGFibGVHRj9GOQ==%;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(); # input 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print(); # input 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(); # input 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print(); # input 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print(); # input 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%;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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEiI0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVFEZGVyaXZhdGl2ZX5hdH4yfmZyb21+dGhlfmRlZmluaXRpb25GJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRic=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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEjZGZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Iy1JI21uR0YkNiRRIjFGJy9GM1Enbm9ybWFsRidGPi1JI21vR0YkNi1RIjtGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjI3Nzc3NzhlbUYnprint(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEjZGZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Iy1JI21uR0YkNiRRIy41RicvRjNRJ25vcm1hbEYnRj4tSSNtb0dGJDYtUSI7RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJw==print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEjZGZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Iy1JI21uR0YkNiRRIy4xRicvRjNRJ25vcm1hbEYnRj4tSSNtb0dGJDYtUSI7RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJw==print(); # input 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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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(); # input 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