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Finding a(2^ln x)/x dx

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(Correction) Radius of Observable Universe

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An example of conservation of momentum in two dimensions.

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We finish the 2-dimensional momentum problem

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2003 AIME II Problem 1

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perfect squares integers square root

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A little trigonometry to figure out the area of a triangle

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Minimum members in a committee

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Probability of moving to a vertex

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Trigonometry and geometry to find the area of an equilateral (but not regular) hexagon

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Finding the sum of the absolute value of the imaginary parts of the square of the roots of a crazy polynomial

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Finding the sum of the absolute value of the imaginary parts of the square of the roots of a crazy polynomial

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Finding the sum of the absolute value of the imaginary parts of the square of the roots of a crazy polynomial

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2003 AIME II Problem 3

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2003 AIME II Problem 4 (part 1)

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Volume of a wedge cut from a cylindrical log

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2003 AIME II Problem 5 Minor Correction

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Finding area of a skewed star

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Area of rhombus from circumradii of triangles

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Sequence from the product of 2 arithmetic sequences

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Sum of polynomial evaluated at roots of another polynomial

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Integration to find average value of a function. Using a graphing calculator to calculate definite integrals.

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Determining whether speed is increasing. Difference between speed and acceleration

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Relationship between velocity and speed and acceleration

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Approximating rate of change and total area under a curve. Trapezoidal sums to approximate integrals

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Second fundamental theorem of calculus application

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Equation of a tangent line and area between curves

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Disk method to find the volume of a solid generated by rotation of a function

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Taking derivatives and integrals of strangely defined functions

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Absolute maximum over an interval. Critical points and differentiability.

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Finding the points of inflection for a strangely defined function

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Mean Value Theorem and differentiability

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Using a tangent line to extrapolate a function from a known initial condition

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Using the second derivative to judge whether an approximation with the tangent line is an overestimate or underestimate

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Solving a differential equation using separation of variables

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Continuity of piecewise-defined functions

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Derivative of a piecewise-defined function

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Average value of a piecewise-defined function on an interval

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Position and slope of particle's path at a given time

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Velocity and acceleration vectors for particle

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Arc length for a curve

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Volume of a solid of rotation and Chain Rule for rates of change.

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Arc length of a function

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Taylor Series approximation of sin(x)

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Taylor Series for cos x at x=0

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Calculating the 6th derivative at 0 from the Taylor Series approximation

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Lagrange error bound for Taylor Polynomial approximation

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** PLEASE NOTE: This is the archived version of the YouTube Live broadcast. The edited video will be posted on Monday. ** Designing an education that truly builds the necessary skills for today's enormously diverse student population is not easy. But it's the key to opportunity for our citizens, economic vitality for our nation, and to assuring the U.S. remains a world leader. There is hope: innovations and innovators that challenge the status quo; research to help us understand how to move the...

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Overview of cycles of regulation, de-regulation and government in 20th century US capitalism

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