Calculus I Calculating limits and derivative
<Text-field style="Heading 1" layout="Heading 1">Limits</Text-field> 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 LCYtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJ4R0YoIiIiLUYkNiMsJkYqRistSSRleHBHRiU2IywkRiohIiJGK0Yz 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<Text-field style="Heading 1" layout="Heading 1">Differentiating</Text-field>
<Text-field style="Heading 2" layout="Heading 2">Symbolic differentiation</Text-field>
<Text-field style="Heading 3" layout="Heading 3">The operator Diff/diff </Text-field> 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 LCQqJkkieEc2IiIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLCQqJEYkIiIjISIiRiYhIiM= 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<Text-field style="Heading 3" layout="Heading 3">The operator</Text-field> 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 Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYpOSRJIm5HRiUiIiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2Iy1JJHNpbkdGMDYjRitGLUYlRiVGJQ== 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 IiIh LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElZGlmZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRImdGJ0YvRjItRjY2JC1GIzYjLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRkQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGTC8lKnN5bW1ldHJpY0dGTC8lKGxhcmdlb3BHRkwvJS5tb3ZhYmxlbGltaXRzR0ZMLyUnYWNjZW50R0ZMLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRidGQUZE LCYqKilJInhHNiJJIm5HRiYiIiJGJ0YoRiUhIiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2Iy1JJHNpbkdGLDYjRiVGKEYoKihGJEYoLUkkY29zR0YsRjJGKEYqRihGKA== 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 LCYqKiksJEkjUGlHJSpwcm90ZWN0ZWRHIyIiIiIiJ0kibkc2IkYpRitGKUYmISIiLUkkZXhwRzYkRidJKF9zeXNsaWJHRiw2IyNGKSIiI0YpRioqKEYkRikiIiRGM0YuRilGMw== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiREYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSJnRicvRjBRJXRydWVGJy9GM1EnaXRhbGljRidGMg== Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqKik5JEkibkdGJSIiIkYtRi5GLCEiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLUkkc2luR0YyNiNGLEYuRi4qKEYrRi4tSSRjb3NHRjJGOEYuRjBGLkYuRiVGJUYl LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiJUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUkmbWZyYWNHRiQ2KC1GLDYlUSUmcGk7RicvRjBRJmZhbHNlRicvRjNRJ25vcm1hbEYnLUYjNiMtSSNtbkdGJDYkUSI2RidGQi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGTy8lKWJldmVsbGVkR0ZBRkI= LCYqKiksJEkjUGlHJSpwcm90ZWN0ZWRHIyIiIiIiJ0kibkc2IkYpRitGKUYmISIiLUkkZXhwRzYkRidJKF9zeXNsaWJHRiw2IyNGKSIiI0YpRioqKEYkRikiIiRGM0YuRilGMw== In this situation operator LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiREYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg== is equivalent with expression 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. JSFH 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 LCQtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kidEdGKCEiIg== 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<Text-field style="Heading 3" layout="Heading 3">Implicit differentiation</Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTA== 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