 ### African Journal of Mathematics and Mathematical Sciences

African Journal of Mathematics and Mathematical Sciences ISSN: 3821-435x Vol. 2 (1), pp. 023-037, January, 2014. © International Scholars Journals

Full Length Research Paper

Christ-Obimba tangent, permutation, sequence and series rules in Calculus

Obimba Kelechukwu Clarence

Department of Biochemistry, School of Science, Federal University of Technology Owerri, P.M.B. 1526, Owerri. Nigeria.  E-mail: kechrisob@yahoo.com; Tel. 07034851899

Accepted 02 January, 2014

Abstract

The aim of this study is to develop a convenient Tangent rule that could be used for determining the area and lengths of sides of a triangle, and also to develop differentiation and integral calculus rules/formulae based on permutation and geometric progression. Christ-Obimba Calculus Rule 1 could be used in determining further/higher derivatives of a function, directly from the parent function, without recourse to the consecutive, previous derivative.  For any triangle (    ) ABC,

,  , and .

a, b, and c are lengths of the sides of the triangle(    ) ABC (Christ-Obimba Tangent Rules).

known as Christ-Obimba Calculus Rules 1 and 2, respectively, could be used in calculus of differentiation, for determining derivatives, and further derivatives of mathematical functions. Parent /root mathematical functions, their consecutive derivatives, and further/higher derivatives, form the Christ-Obimba geometric progression sequence in calculus, given by :

The Christ-Obimba geometric progression series in calculus could be used to obtain all the derivatives, of the parent function of a finite series, without calculating individual derivatives, singly.

m = the specific derivative (1st, or 2nd or 3rd…….or mth derivative).

n = index power to which the variable x is raised. e.g : x4 (n = 4).

a = constant = coefficient of the variable term in xn.

C = constant.

T1 =the first term of the geometric progression series of calculus = axn.

Ti = the dependent variable y; Td = the term in the independent variable x.

Key Words: Tangent, calculus, permutation, geometric progression series, derivatives.

### List of Other Journals

International Journal of Law and Legal Studies
Advanced Journal of Environmental Science and Technology
Advances in Agriculture and Agricultural Sciences
Advances in Aquaculture and Fisheries Management
Advances in Food Science and Technology
African Journal of Agricultural Economics and Rural Development
African Journal of Agricultural Marketing
African Journal of Agriculture
See all Journals

Viewing Options: