Indeterminate forms

A form, whose value cannot be evaluated is called an indeterminate form.

Introduction

In mathematics, the numbers are often appeared in various acceptable forms. The values for most of the forms can be calculated but there are some forms, which cannot be determined mathematically. Hence, the forms are called indeterminate forms.

Examples

Let’s learn each indeterminate form with understandable example.

$(1).\,\,\,$ $\dfrac{0}{0}$

The number zero is introduced to represent nothing. Dividing the zero by zero means nothing is divided by nothing. So, the quotient of zero by zero is indeterminate.

$(2).\,\,\,$ $\dfrac{\infty}{\infty}$

The symbol infinity is introduced in mathematics for writing an inexpressible quantity. Dividing an inexpressible quantity by another inexpressible quantity is meaningless. So, the quotient of infinity by infinity is indeterminate.

$(3).\,\,\,$ $\infty^0$

$(4).\,\,\,$ $0^\infty$

$(5).\,\,\,$ $0^0$

$(6).\,\,\,$ $\infty^\infty$

$(7).\,\,\,$ $1^\infty$

$(8).\,\,\,$ $\infty-\infty$