Did you know that a corner in the original continuous function means a jump discontinuity in the derivative? Raelene explains why using multiple ways of representing a corner: verbal, numerical, graphical an algebraic....

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Raelene relates the derivative to the slope of a tangent line, talks about what it means for a function to have a derivative, shows 3 functions that do not have a derivative at the origin and shows three basic formulas for the derivative using limits....

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Raelene discusses what it means for a function to be differentiable at a point, zooms in at the origin on the graphs of 3 functions that are NOT differentiable and works through an example of how to make a piecewise function differentiable....

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Raelene discusses piecewise functions that are defined using absolute value or using two or more expressions defined on subdomains of the real numbers. See various examples of piecewise functions that are continuous or discontinuous, from algebraic and gr...

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Raelene introduces new characters in the family of basic graphs: y = sinx /x, (cosx - 1) / x and (e^x - 1)/x and uses multiple ways to explain how they all have a hole at x = 0.
There is an error at 0:20 when Raelene says that f(x) has odd symmetry, but ...

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Raelene introduces the cast of "The Discontinuities": the parent graphs with holes, jumps, vertical asymptotes and oscillating discontinuities. A few children of the parent hole and jump functions make guest appearances in this episode: some examples of t...

From Raelene Math

Raelene explains the meaning of and gives a few strategies to evaluate the limit as x approaches 2 on the function f(x) = |6x-12|/(4-2x) using technology and the Rule of Four: verbal, numerical, graphical and algebraic. This video is a must see to deepen ...

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Raelene explains limits as x approaches 0, -∞ and +∞ on the function f(x) = (sinx)/x using technology and the Rule of Four: verbal, numerical, graphical and algebraic. This video is a must see to deepen your understanding of limits....

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What is a limit value? A limit value is the height that y approaches on a graph as x approaches an x-coordinate. The foundation of learning limits is to understand how limit values differ from function values, which requires understanding discontinuities....

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Projectile motion is the motion of an object in two dimensions subject only to the force of gravity. This video follows from "You'll Fall for Free Fall". Both videos look at position, velocity and acceleration using the Rule of Four: verbally, numerically...

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People's intuition on free-fall motion is often different from their calculations using formulas. This video shows you multiple ways to represent the kinematic quantities of free fall (position, velocity and acceleration), challenges your intuition about ...

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This video works out an example of Newton's Second Law and a system of two ropes and a hanging mass in equilibrium. The unknowns are two tension magnitudes, which requires the solution of a system of simultaneous equations....

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Raelene explains how to determine the domain of any function, considering four domain restrictions by thinking verbally, numerically, graphically and algebraically. This video presents a conceptual understanding of undefined values. Why are √(-5), log(-...

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This video looks at position, velocity, acceleration, speed and distance of a particle in one dimension (say, traveling along a horizontal line: right, left, right) and relates the concepts by derivatives and represents the quantities graphically and alg...

From Raelene Math

Graphically, the Intermediate Value Theorem states that between any two known y-coordinates on a continuous function, every other (y) value in between (intermediate) to those known values is part of the range of the function, and so there is a correspondi...

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This video defines rational functions and their characteristics such as intercepts, discontinuities like vertical asymptotes and holes in the graph as well as end behaviour (or zoomed out behaviour), collectively referred to as "non-vertical asymptotes" (...

From Raelene Math

The shape that a graph looks like on the left and right ends when you zoom out far enough (let x approach -∞ or +∞) is called an "end behaviour asymptote" or "zoomed out asymptote" or non-vertical asymptote, non-VA. For rational functions, some exampl...

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This video graphs rational functions using sign charts and considers the features of x and y intercepts, discontinuities (holes and vertical asymptotes) and end behaviour (or "non-vertical" or "zoomed out") asymptotes (such as horizontal, slant or parabol...

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This video follows from the video "Transformations of Functions and Curves: A Better Way", and looks at two examples of parametrically and vector-defined curves and graph them in the xy-plane by several methods: making a table of values, eliminating the p...

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This video looks at transformations in an updated way, discussing why we often "do the opposite for x" but NOT for y and presents a better way to transform parent graphs, for both functions AND relations....

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This video looks at a vector in the plane and creates: (1) parallel and orthogonal unit vectors to the given vector; (2) a family of vectors that is parallel to the given vector; and (3) a vector equation for the line passing through a point (h,k) and par...

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This video shows an example of 2D vectors, converting forms between rectangular and polar components, sketching vectors and forming linear combinations of vectors....

From Raelene Math

This video takes a quick tour from 2 points in the plane to a line of best fit, slope-intercept and intercept forms of the line, to forming a right triangle, a vector and the radius of a circle from the hypotenuse, to writing the equation of that circle u...

From Raelene Math