More Maple Commands - IIFirst, a few things from last time. QyQ+SSJmRzYiLCYqJEkieEdGJSIiJyIiIiIiJkYqRio=Notation for higher derivatives of expressions QyQtSSVkaWZmRyUqcHJvdGVjdGVkRzYkSSJmRzYiLUkiJEdGJTYkSSJ4R0YoIiIjIiIiTaylor seriesQyQtSSd0YXlsb3JHJSpwcm90ZWN0ZWRHNiUtSSRleHBHNiRGJUkoX3N5c2xpYkc2IjYjSSJ4R0YrL0YtIiIiIiIjRi8=In the lecture, we will discuss the meaning of the O() term. QyQtSSVldmFsRyUqcHJvdGVjdGVkRzYkSSIlRzYiL0kieEdGKCQiIzchIiIiIiI=QyQtSSZldmFsZkclKnByb3RlY3RlZEc2I0kiJUc2IiIiIg==
<Text-field style="Heading 1" layout="Heading 1">Plotting</Text-field>You can plot parametrized curvesQyQtSSVwbG90RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiM3JS1JJHNpbkdGKDYjSSJ0R0YoLUkkY29zR0YlRi0vRi47IiIhLCRJI1BpR0YmIiIjIiIiYou can limit the y extent of the graph as well as the x extent.LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYlLUkkZXhwR0YkNiNJInhHRicvRiw7IiIhIiM1L0kieUdGJztGLyIiIw==This is useful to plot functions with singularitiesQyQtSSVwbG90RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQtSSR0YW5HRiU2I0kieEdGKC9GLTsiIiEiIzUiIiI=QyQtSSVwbG90RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiUtSSR0YW5HRiU2I0kieEdGKC9GLTsiIiEiIzUvSSJ5R0YoOyEiJSIiJSIiIg==QyQtSSVwbG90RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiYtSSR0YW5HRiU2I0kieEdGKC9GLTsiIiEiIzUvSSJ5R0YoOyEiJSIiJS9JKGRpc2NvbnRHRihJJXRydWVHRiYiIiI=You can put multiple plots on the same graph and distinguish them using colours and styles.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LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYlKiRJInhHRiciIiQvRio7IiIhIiIiL0kqdGhpY2tuZXNzR0YnRis=
<Text-field style="Heading 1" layout="Heading 1">Taylor Series Graphically</Text-field>Consider again the Taylor series of f(x) = exp(x) at x=1QyQ+SSJmRzYiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiNJInhHRiUiIiI=QyQtSSd0YXlsb3JHJSpwcm90ZWN0ZWRHNiVJImZHNiIvSSJ4R0YoIiIiIiIjRis=QyQ+SSNUMUc2Ii1JKGNvbnZlcnRHJSpwcm90ZWN0ZWRHNiRJIiVHRiVJKHBvbHlub21HRigiIiI=LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkNyRJImZHRidJI1QxR0YnL0kieEdGJzsiIiEiIiM=T1 is just the tangent line Let's get a closer look.LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkNyRJImZHRidJI1QxR0YnL0kieEdGJzskIiIqISIiJCIjNkYxHard to see anything, let's look at the differenceLUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLCZJImZHRiciIiJJI1QxR0YnISIiL0kieEdGJzskIiIqRi0kIiM2Ri0=Let's go to the next ordersPyhJIm9HNiIiIiJGJSIiJUkldHJ1ZUclKnByb3RlY3RlZEc+JkkiVEdGJDYjRiMtSShjb252ZXJ0R0YoNiQtSSd0YXlsb3JHRig2JUkiZkdGJC9JInhHRiRGJSwmRiNGJUYlRiVJKHBvbHlub21HRig=LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYlNydJImZHRicmSSJUR0YnNiMiIiImRiw2IyIiIyZGLDYjIiIkJkYsNiMiIiUvSSJ4R0YnOyIiIUYxL0kmY29sb3JHRic3J0kkcmVkR0YnSSZncmVlbkdGJ0klYmx1ZUdGJ0kmYmxhY2tHRidJJ3llbGxvd0dGJw==Again let's zoom in a bit and look at differencesLUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkNyYsJkkiZkdGJyIiIiZJIlRHRic2I0YsISIiLCZGK0YsJkYuNiMiIiNGMCwmRitGLCZGLjYjIiIkRjAsJkYrRiwmRi42IyIiJUYwL0kieEdGJzskIiIqRjAkIiM2RjA=LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkNyQsJkkiZkdGJyIiIiZJIlRHRic2IyIiJCEiIiwmRitGLCZGLjYjIiIlRjEvSSJ4R0YnOyQiIipGMSQiIzZGMQ==