Mathematics Magazine for Grades 1-12  

 

5/2004

     

“Get your mind accustomed to doubting and your heart to being conciliatory.” - George Christoph Lichtenberg

Grade 12

Theory:

Polynomial function

A function whose value is given by the sum of whole-number powers of the variable, each multiplied by a real-number coefficient, eg:
f(x) = x4 +3x + 1
f(x) = 5x2 + x
f(x) = 10x57+3x16+12x5

Solutions from the Previous Issue: 

Proposed by Mihai Rosu Professor Toronto.

Simplify the following expressions:

1.        E= .

Solution:

E=

. We used: .

2.       

Solution:

We have    and

Hence =2+3+4+…+n=

= .

3.       

Solution:

We have

4.       

Solution:

.

Proposed Exercises: 

Prposed by Mihai Rosu Professor Toronto

  1. Prove that the line  is tangent to the hyperbola . Find the point of contact.
  2. Find the equation of a tangent to the parabola    at the point (2,4).
  3. Find the equation of a tangent to the parabola    from the point (-1, ).
  4. Find the equation of the tangents with slope 2  to the ellipse .