0 ÷ 1 and 1 ÷ 0 | Undefined form | Indeterminate form | скачать в хорошем качестве

0 ÷ 1 and 1 ÷ 0 | Undefined form | Indeterminate form |

0 ÷ 1 and 1 ÷ 0 | Prove that 0 ÷ 1 = 0 and 1 ÷ 0 = undefined | Defined and undefined form | Indeterminate form | Dear viewers, it is my pleasure to deliver you mathematics tutorials in simple and native language so that you can get it easily. #Maths Made Easy is a channel where you can improve your #Mathematics. The two numbers can not be compared because 0/1 = 0 and 1/0 is #indeterminate. 0/1 is 0 because it is one of the properties of 0 that 0 divided by any nonzero number is 0. 1/0 is indeterminate because the product of any quotient with zero is zero where as what we should have as dividend is 1. In calculus and other branches of mathematical analysis, limits involving an algebraic combination of functions in an independent variable may often be evaluated by replacing these functions by their limits; if the expression obtained after this substitution does not provide sufficient information to determine the original limit, then the expression is called an indeterminate form. More specifically, an indeterminate form is a mathematical expression involving at most two of 0, 1 and infinity obtained by applying the algebraic limit theorem in the process of attempting to determine a limit, which fails to restrict that limit to one specific value or infinity, and thus does not determine the limit being sought. A limit confirmed to be infinity is not indeterminate since it has been determined to have a specific value (infinity).[1] The term was originally introduced by Cauchy's student Moigno in the middle of the 19th century. There are seven indeterminate forms which are typically considered in the literature. The most common example of an indeterminate form occurs when determining the limit of the ratio of two functions, in which both of these functions tend to zero in the limit, and is referred to as "the indeterminate form 0/0 Not every undefined algebraic expression corresponds to an indeterminate form.[2] For example, the expression {\displaystyle 1/0}1/0 is undefined as a real number but does not correspond to an indeterminate form; any defined limit that gives rise to this form will diverge to infinity. An expression that arises by ways other than applying the algebraic limit theorem may have the same form of an indeterminate form. However it is not appropriate to call an expression "indeterminate form" if the expression is made outside the context of determining limits.