CALENG1

Graphing Polynomial Functions Using End Behavior, Zeros, and Multiplicities. Mario’s Math Tutoring.

This video evinces how to graph a polynomial function by using the end behavior, zeroes, and multiplicities of the said function. It is a simple method of sketching the graph of a polynomial function. Note: It is just a rough sketch meant to show what the graph looks like.

Graphing Polynomial Using Rational Zero Theorem, Descartes Rule of Signs, Synthetic Division. Mario’s Math Tutoring.

This video is pertinent to the first video. However, it shows how the roots of the function are determined by using the Rational Zero Theorem, Descartes Rule of Signs, and Synthetic Division. These methods are used in lieu of factoring (i.e., equations that cannot be done by factoring).

Note: Try to factor it out. If not plausible, then proceed to the said methods.

Descartes Rule of Signs. Mario’s Math Tutoring.

This video further explains how Descartes' Rule of Signs works. It helps to narrow down the number of options to be used in the synthetic division. It will improve the efficiency of the trial-and-error method.

Graphing Rational Function Step-by-Step (Completer Guide 3 Examples). Mario’s Math Tutoring.

This video clearly shows the step-by-step procedure of graphing a rational function. It also illustrates how to graph the three different cases of the said function by using the sign analysis that will be further explained in the video.

Sketching Rational Functions Step by Step (6 Examples!). Mario’s Math Tutoring.

The indicated video presents more examples of sketching rational functions in a step-by-step way. Practice makes perfect!

Conic Sections – Circles, Ellipses, Parabolas, Hyperbola – How To Graph & Write in Standard Form. The Organic Chemistry Tutor.

The said link illustrates how to graph and write conic sections (Circles, Ellipses, Parabolas, Hyperbola). This will help you understand the fundamental knowledge that will be needed when you go to advanced Calculus classes.

Formal definition of limits Part 1: Intuition Review, Khan Academy

This video introduces the basic idea about the definition of limits. It is the first of a 4-part video series. As such, please watch the proceeding parts to further grasp the idea.

Formal definition of limits Part 2: building the idea, Khan Academy

This is the part 2 of the prior video. It envices the idea behind the formal definition (i.e., the epsilon-delta) of limits. Likewise, please watch the subsequent two videos.

Formal definition of limits Part 3: the definition, Khan Academy

This video illustrates how the building idea supports the formation of the mathematical definition of limits. The epsilon-delta definition pertains to the formal definition of the aforementioned topic. Watch the next video to further understand them via an example.

Formal definition of limits Part 4: using the definition, Khan Academy

This video evinces the proving of limits using the epsilon-delta definition. With the use of example, it clearly depicts how the mathematical formula proved the limits.

Continuity Basic Introduction, Point, Infinite, & Jump Discontinuity, Removable & Nonremovable, The Organic Chemistry Tutor

This video explains what continuity is. It also illustrates the different types of discontinuity: Point, Infinite, & Jump Discontinuity. Furthermore, the video classifies them as either removable or nonremovable discontinuities.

3 Step Continuity Test, Discontinuity, Piecewise Functions & Limits, The Organic Chemistry Tutor

This video shows how to determine the points of discontinuity and to prove whether a function is continuous or discontinuous at a certain point. The video used the 3 step continuity test that will be further explained as you watch it.