Function Graphs

Function Graphs: Level 4 Challenges


Given the equation 4x2+23xy+2y2=14x^2+2\sqrt{3}xy+2y^2=1.
Through what angles θ[0,π]\theta \in [0,\pi] should the axes be rotated so that the term xyxy is removed from the transformed equation?

Give the answer as the sum of all values of θ\theta(in degrees).

The graph above shows the figure created by the function x2+(y+x)2=1x^2+(y+x)^2=1.

Find the area of this tilted ellipse correct to 2 decimal places.

For each integer n>1n>1, let F(n)F(n) be the number of solutions to the equation sinx=sin(nx)\sin{x} = \sin{(nx)} on the interval [0,π][0,\pi]. What is n=22007\displaystyle\sum_{n=2}^{2007}F(n)F(n)?

If f(x)=x21cosxf(x)=\dfrac{x^2}{1-\cos x}, where 0<x<10<x<1. Which of the following describes the function of f(x)f(x) ?

If f(x)f(x) and g(x) g(x) have the same fundamental period, then so does f(x)+g(x) f(x) + g(x) .


Problem Loading...

Note Loading...

Set Loading...