MATRIKS DIAGONAL DALAM KAJIAN PENYELESAIAN SISTEM PERSAMAAN DIFERENSIAL - Nurman, Try Azisah (Teknosains: Media Informasi Sains dan Teknologi, 2014)
This paper discusses the methods of algebraic functions on the settlement limit of indeterminate forms. Limit is a mathematical method used to describe the effect of variable functions move closer to a point on a particular function. The goal is to determine the specific characteristics of the methods of algebraic functions on the settlement limit of indeterminate forms. The methods used is a special method that consists of factoring methods, methods of multiplication herd, and the division with the highest rank method, and the method of L’ Hopital. By using the methods mentioned above, then we obtain the specific characteristics of the methods of algebraic functions settlement limit on the indeterminate form are 1. Factoring methods: (a) The numerator is the result of squaring the binomial equation of the denominator. Where, (i) If the binomial equation using the difference operation, then its points is positive. (ii) If the binomial equations using addition operation, then its points is negative. (b) the constant factor of each of the numerator and denominator equally. One of which is a three tribal equation in the form ax2 + bx + c , the value of b it is the sum of the value of the constant multiplication. (c) If the numerator and denominator are both binomial equations with difference operation, where the variables and constants in the numerator is the square of the variable and constant denominator. Or conversely, variables and constants in the denominator is the square of the variable and constant numerator. (d) If the equation is a difference of two fractions where the denominator is a binomial variables and constants in the denominator is the result of one of the squaring of the variables and constants in the denominator of the other. (e) If the equation in the form of fragments which all contain the same variables. (f) If the equation is in the form of two parts, where the coefficients and constants in the numerator or the same multiplication factor, so that when the coefficients and constants removed it will form one of the factors that equation equal to that of the denominator. 2. A herd Multiplication method: (a) If the equation is the difference of two roots. (b) If the equation in the form of the difference or fractions containing amount root form. Both the numerator and the denominator. 3. Distribution by Top Rank methods: (a) If the equation in the form ∞/∞. (b) If a polynomial equation of degree 3, 4, 5,... etc. Which is hard to be factored. 4. L’ Hopital method: if the limit point is substituted then produces the indeterminate form 0/0, ∞/∞, ∞-∞ , except if the derivative of the function at the root of the denominator in the form similar to the form factor function in the numerator. Vice versa, the derivative of the function at the root of the numerator shaped form factor similar to the function in the denominator.