Indefinite integrals

If you need to calculate the distance travelled when you know the velocity as a function of time , since s'(t) = v(t) you need to be able to perform antiderivation i.e. finding a function whose derivative equals your function. … Läs mer

Differentiating the natural logarithm, products and quotients

In order to be able to deduce the derivative of the natural logarithm we resort to using implicit differentiation. Let x= ey(x) Differentiating both sides gives dx/dx = d ey(x)/dx 1=ey(x) dy(x)/dx Solving for dy(x)/dx one obtains dy(x)/dx = 1/ey(x) … Läs mer

Pi-day

March the 14th. has officially been named the international π-day to honour this magical number which equals the ratio of the circmference to the diameter for all circles. http://www.wikihow.com/Celebrate-Pi-Day In 1882 the german mathematician Ferdinand Lindemann showed that pi is … Läs mer

Publicerat i Geometri, Gymnasiematematik(high school math) | Lämna en kommentar

Differentiation of the trigonometric functions

To be able to differentiate the trigonometric functions one needs some standard limits: With the aid of these and the definition of the derivative it is possible to show that f(x)= sin (x) implies  f ‘(x) = cos(x) and f(x) … Läs mer

Publicerat i Calculus, Gymnasiematematik(high school math), matematik 4 | Märkt | Lämna en kommentar

Radians and an attempt at squaring the circle

That one rotation equals 360 degrees is just a convention, There is nothing partcular about 360 except that it can be divided by many numbers. Another, and a more fruitful, approach to measuring angles is to use the length of … Läs mer

Publicerat i Geometri, Gymnasiematematik(high school math) | Lämna en kommentar