# The Pamphlet Collection of Sir Robert Stout: Volume 50

# University of New Zeland. — Mathematics. — Paper b. Algebra, Trigonometry, &c

## University of New Zeland.

## Mathematics.

##
Paper *b*. Algebra, Trigonometry, &c.

1. Determine when *x*^{n}+*a*^{n} is divisible by *x* + *a*.

Find the values of A and B that *x*^{n}−A*x*^{2}+B may be divisible without remainder by *x*^{2}−*x*−2.

2. Assuming the Binomial Theorem true for a positive integral index, prove it true generally.

Prove that, squares and products of *x, y* above the second degree being neglected,

3. State and prove the principle of proportional parts for logarithmic tables.

Prove that

4. Sum the series

page 25. Investigate the solution of the triangle in which A, *a, c* are given.

Find the distance between the centres of the circles inscribed in the two triangles satisfying the given conditions in terms of A, *a, c.*

6. Investigate Demoivre's Theorem, finding *all* the values of

7. Find any series suitable for the calculation of π Show that

8. Sum the series

9. Investigate the complete conditions for a maximum or minimum value of a function of one independent variable.

Examples:

10. Investigate the formula for integrating by parts. Integrate the following expressions:—