How to Find the Limits of Polynomial Functions Using Tables, Graphs, and Analytic Techniques

One of the first topics that is covered in a Calculus course is how to find the limits of polynomial functions. Constant, linear, quadratic, and cubic functions are all examples of polynomial functions. The coefficients of the terms of a polynomial function can be positive or negative, and the exponents of all of the terms must be integers greater than or equal to zero.

You can view the PDF handout by clicking this link, Limits of Polynomial Functions, or you can right-click and save the PDF to your computer so you can reference it later. The handout presents the theorem that governs the limits of polynomial functions and then presents five examples in ascending order of complexity. Each limit is determined analytically by applying the theorem, and the result is supported numerically by a table of data and graphically by a plot of the function of which the limit is being taken.

Determining the limit of a polynomial function is a very straightforward 2-step process.

  1. Determine that the function is a polynomial.
  2. Evaluate the polynomial at the value being approached.

The following video walks through four of the examples in the handout. The handout includes a more detailed explanation and step by step solutions. While watching the video, pausing the video can allow more time to look at the examples and the solutions.

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How to Derive the Quadratic Formula by Solving the Quadratic Equation

This video shows how to derive the quadratic formula by solving the quadratic equation.

This is a step by step solution starting with the quadratic equation.

1) divide through by the coefficient “a”

2) complete the square by adding “b^2/(4*a^2)” to both sides

3) subtract “c/a” from both sides of the equation

4) take the square root of both sides of the equation (don’t forget the plus or minus +/- in front of the square root.)

5) combine the fractions under the square root

6) subtract “b/a” from both sides of the equation

7) combine the fractions

We have successfully isolated “x” and therefore derived the quadratic formula from the quadratic equation.