Constant Rule Teacher Resources
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Calculus: Derivatives 3
This video covers the differential notation dy/dx and generalizes the rule for finding the derivative of any polynomial. It also extends the notion of the derivatives covered in the Khan Academy videos, ï¿½Calculus Derivatives 2ï¿½ and ï¿½Calculus Derivatives 2.5 (HD).ï¿½ Note: Additional practice using the power rule for differentiating polynomials (including some with negative exponents) is available to the listener.
Calculus: Derivative of x^(x^x)
Sal starts with an example of finding dy/dx of y = x2 and builds to showing the solution to the more complicated implicit differentiation problem of finding the derivative of y in terms of x of y = x ^ x ^ x .
L'Hopital's Rule Example 2
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.
Equation of a tangent line
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 investigate derivatives. In this calculus instructional activity, 12th graders use technology to explore the basic derivatives and how to choose the proper formula to use them. The instructional activity requires the use of the TI-89 or Voyage and the appropriate application.
Graphs of Functions and Their Derivatives
Students practice the concept of graphing associated to a function with its derivative. They define the concepts of increasing and decreasing function behavior and explore graphical and symbolic designs to show why the derivative can be used as an indicator for the behavior.
Time Constant Calculations
In this time constant worksheet, students answer 52 questions about the rate of current changes and voltage changes in capacitors. They analyze circuits and determine the time it takes for capacitors to change voltage and they specify voltages at specified times.
Time Constant Circuits
In this time constant circuits learning exercise, students answer 23 questions about the design of circuits that need time delays, about capacitors and inductors, and about resistors and the design of circuits.
In this calculus learning exercise, students solve functions using the derivative formulas. There are 26 formulas for them to review and go over.
AP Calculus Practice Exam BC Version: Part B
In this calculus worksheet, learners solve 17 multiple choice problems. Students find limits, summations, and derivatives of functions. Learners find the area of an enclosed region between two curves.
Graph And Their Derived Function
Students analyze graphs and determine their general shape. In this calculus instructional activity, students solve functions by taking the derivative, sketch tangent lines and estimate the slope of the line using the derivative. They graph and analyze their answers.
In this calculus worksheet, students use integration to solve word problems they differentiate between integration and anti derivatives, and between definite and indefinite integrals. There are 3 questions with an answer key.
Even More Calculus
In this calculus worksheet, 12th graders differentiate and integrate basic trigonometric functions, calculate rates of change, and integrate by substitution and by parts. The twenty-two page worksheet contains explanation of the topic, numerous worked examples, and sixteen multi-part practice problems. Answers are not provided.
AP Calculus Practice Exam
In this Calculus learning exercise, 12th graders are provided with practice problems for their exam. Topics covered include limits, derivatives, area bounded by a curve, minimization of cost, and the volume of a solid of revolution. The four page document contains seventeen multiple choice questions. Answers are not included.
Seventeen Multiple Choice Calculator AP Calculus BC Practice Test
In this AP Calculus BC worksheet, students answer seventeen multiple choice questions with the use of a calculator. The questions are a fifty minutes times practice test for the AP exam.
AP Calculus Practice Exam BC Version- Section I -Part B
In this AP Calculus Practice Exam worksheet, students solve seventeen multiple-choice questions using a graphing calculator. This BC practice test is designed to be finished in fifty minutes.
A.P. Calculus Practice Exam BC Version Section I Part B
In this AP Calculus practice test worksheet, students prepare for the BC version on the test by solving seventeen multiple-choice questions using a calculator. The test should be timed and 50 minutes in length.
Limits and Derivatives
For this calculus worksheet, students evaluate functions and solve problems using the derivative. They apply the rules of limits to solve functions where the limit of x approaches zero. There are 12 problems to solve.
Calculus for electric circuits
In this circuits activity students complete a series of questions on equations, robotics and integration. There is an answer sheet.
Parametric, Vector, Polar, and 3D Functions
Twelfth graders investigate the capabilities of the TI-89. In this calculus lesson, 12th graders explore the parametric equation for a circle, for arc length of curves, and for trajectories. Students investigate the symbolic and graphical representation of vectors. Students use polar functions of investigate the area bounded by a curve. Students investigate a 3D graphing application.