Example of how to apply the formula for solving quadratic equations

Example of how to apply the formula for solving quadratic equations

We investigate a small piece of area in a 2D region. We justify pictorially, the factor of r in the form dA = r dr theta. The Jacobian determinant is given for circular polars, which is then shown to yield r as the appropriate factor in the area dA.

Completes examples on differentiating simple functions and provides practice questions and answers at the end for viewer to work on themselves.

Completes 3 examples of differentiating constants and explains why they differentiate to zero. Completes 3 examples of differentiating simple functions.

Defines basic rule for differentiation and completes 3 basic examples involving x to a power of 2 or greater, then completes 3 more examples, this time all with x to the power of 1.

We discuss combinations of even and odd functions involving sums, products etc and investigate their odd and even properties. We show the use of such properties in reducing the work needed to evaluate a certain kind of integral.

We extend the expansion of the nth power of a binomial and investigate the power series for the nth power of (1+x). For all n, Infinite Maclaurin series are obtained and the coefficients identified. We revisit part 1 where n is positive integer.

Positive integer powers of the binomial (a+b) are examined. It is shown how to expand the brackets to obtain a finite series using coefficients from the Pascal triangle. Later these coefficients are identified as the nCr coefficients.

Shows two incorrect solutions to finding the derivative of (3x+5)^2x and discusses why they are incorrect. The correct approach is then explained.