logarithms and exponentials

Introduction - In this chapter, we shall study two series known as the Exponential series and Logarithmic series. In our discussion, we shall make use of mathematical tools like formula for sum of an infinite G.P., combinatorial coefficient..

In this chapter, we shall study two series known as the Exponential series and Logarithmic series. In our discussion, we shall make use of mathematical tools like formula for sum of an infinite G.P., combinatorial coefficients, the inequality 2 n - 1 n! for n N etc.In this chapt..

The sum of the infinite series 1 + 1/1! + 1/2! + 1/3! + 1/4! + ... is called the exponential number. If x is any complex number then the series is called the exponential series. It can be proved mathematically that this exponential series has a sum and ..

During this period growth begins slowly at first and becomes rapid later on. Hence the curve rises steeply. As a result the organism enlarges doubling and redoubling in size. This phase is also called as logarithmic pha..

. Sigmoid growth curve is formed of five phases. a) Lag phase b) Positive acceleration phase c) Logarithmic or exponential phase d) Negative acceleration phase e) Stationary phase. a) Lag phase - Period where individuals adapt to the new environment. b) Positive acceleration pha..

Name the function f ( x ) = 7 e - 8 x . => Power function or Logarithmic function or Exponential decay function or Exponential growth function..

The function f ( x ) = 9 · 3 x is______. => A constant function or A logarithmic function or A power function or An exponential function..

Fundamentals of Equations Algebraic and transcendental equations; If f(x) is a polynomial in x, then f(x) =0 is an algebraic equation. Example; x 7 + 5x - 2=0. If f(x) contains algebraic and non algebraic functions namely exponential, logarithmic, trigonometric and inv..

Absolute value to solve equations/inequalities Systems of linear equations/inequalities Operations on polynomials Factoring polynomials/trinomials Operations on complex numbers Operations on rational expressions Graphing quadratic equations Quadratic equations in complex number system Qua..

(x) of x under f is called the value of 'f ' at x. Types of Function and their Graphs: Constant function, Identity function, Polynomial function, Modulus function, Square root function, Greatest integer function or Step function (Floor function), Smallest integer function (Ceiling function), E..