LHospitals Rule Short Topic 6 Presented by Lin
L’Hospital’s Rule Short Topic 6 Presented by Lin Mc. Mullin Mass Insight Fall Conference November 2020
L’Hospital’s Rule Theorem (L’Hospital’s Rule) If f and g are differentiable functions and f(a) = g(a) = 0, Then , if this limit exist.
L’Hospital’s Rule What does f(a) = g(a) = 0 tell you about f and g? The functions intersect on the x-axis at (a, 0)
L’Hospital’s Rule First observation: Local linearity is a property of differentiable functions that says if you zoom in at a point on the graph (with equal zoom scaling in both directions), eventually the graphs will appear linear (look like a straight line). Try it: graph your favorite differentiable function and zoom in on a points several times. What do you see?
L’Hospital’s Rule Second observation: Consider two lines: Where do they intersect? What is the ratio On the x-axis at (a, 0)
L’Hospital’s Rule Let’s look at Kind of looks like lines If they were lines, what’s the ratio of their y-coordinates?
L’Hospital’s Rule Let’s look at Kind of looks like lines again If they were lines, what’s the ratio of their y-coordinates?
L’Hospital’s Rule Let’s look at Kind of looks like lines again If they were lines, what’s the ratio of their y-coordinates?
L’Hospital’s Rule The local linear approximation of a function is given by Therefore, near x = a, if
L’Hospital’s Rule 2012 BC 28 2018 AB 9
L’Hospital’s Rule 2018 BC 3 2018 AB 19
L’Hospital’s Rule 2019 FR AB 3(d)
L’Hospital’s Rule
L’Hospital’s Rule
L’Hospital’s Rule Left: Johann Bernoulli (1667 – 1748) Right: Guillaume-François-Antoine Marquis de l'Hôpital, Marquis de Sainte. Mesme, Comte d'Entremont, and Seigneur d'Ouques-la-Chaise (1661 – 1704)
L’Hospital’s Rule Short Topic 6 Presented by Lin Mc. Mullin Mass Insight Fall Conference November 2020
Welcome! • Lin Mc. Mullin • Moderator, AP Calculus Community Short Talk: L’Hospital’s Rule • AP Calculus AB & BC teacher for 30 years • AP Consultant since 1991 • National Director of Mathematical Programs for the National Math and Science Initiative (2008 – 20012) • Author of Teaching AP Calculus • Blogger at Teaching. Calculus. com • Links to resources for this session and a copy of the Power. Point slides may be found here www. Teaching. Calculus. com > Presentations > Mass Insight 17
L’Hospital’s Rule
- Slides: 18
