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- Kimberly K.
- Bourbonnais, IL
Differentiation Teacher Resources
Find teacher approved Differentiation educational resource ideas and activities
Sal shows two different ways of finding the limit of a rational expression where the limit of the polynomial is of an indeterminate form involving infinity. First, he shows how to solve this using Lï¿½Hopitalï¿½s Rule and then by using the factoring method to solve for the limit algebraically. Note: Practice problems on Lï¿½Hopitalï¿½s rule are available and can be practiced now or after watching the other example videos.
In this video, Sal starts with an example where the limit is not indeterminate but rather undefined and therefore cannot be solved using Lï¿½Hoptialï¿½s rule. He shows how you can rewrite the problem algebraically so that the rule can be applied. Note: Practice problems on Lï¿½Hopitalï¿½s rule are available.
Sal shows the complex solution to a challenging derivative problem about ï¿½normalinesï¿½. This is probably beyond the scope of most first year calculus students but might be an interesting problem to show how complex these problems can get. Most of the thorny computations shown utilize techniques learned in algebra, but the notation used and the multifaceted parts of the problem make it quite involved.
Using a specific example, Sal shows how to find the equation of a tangent line to a given function at a specific point. Specifically, he solves the problem of finding the tangent line to the function f(x) = xex at x = 1. This problem provides a review of the product rule, slope-intercept form of a line, and steps for finding the equation of a line. It also, provides a nice visual understanding of the problem by graphing both the original equation and the found tangent line.
Twelfth graders explore differential equations. In this calculus instructional activity, 12th graders explore Euler’s Methods of solving differential equations. Students use the symbolic capacity of the TI-89 to compare Euler’s Method of numeric solutions to a graphical solution.
In this calculus instructional activity, students solve 10 different problems that include determining the first derivative in each. First, they apply properties of logarithmic functions to expand the right side of each equation. Then, students differentiate both sides with respect to x,using the chain rule on the left side and the product rule on the right. In addition, they multiply both sides by y and substitute.