Indeterminate value in functions

Indeterminate Value in Functions

» Functions evaluate to 0000

→ eg: x2-4x-2∣x=2=00x2−4x−2∣x=2=00

*Though the function evaluates to 0000, it may take a value.*

evaluating a function

Consider the value of function f(x)=x2-1x-1f(x)=x2−1x−1 when x=2.2x=2.2.

On substituting x=2.2, we get f(2.2)=2.22-12.2-1.

f(2.2)=3.2

function evaluating to 0/0

Consider the value of function f(x)=x2-1x-1 when x=1

On substituting x=1, we get

f(1)

=12-11-1

=00

That is, the function evaluates to indeterminate value when x=1.

Let us closely examine the function f(x)=x2-1x-1.

The numerator be factorized as x2-1=(x+1)(x-1)

Rewriting the function f(x)=x2-1x-1 as the function f(x)=(x+1)(x-1)x-1.

It is noted that the function can be simplified to f(x)=x+1 when x≠1. Note that 0 cannot be canceled out in expressions or equations.

So the given function

f(x)

=x+1 when x≠1

=x2-1x-1 when x=1

By this it is concluded that f(x)∣x=1 is indeterminate value 00.

Many students wrongly understand that the algebraic simplification (like canceling x-1 in the example above) solves the indeterminate value. It is not so -- the function remains indeterminate at that input value x=1.

another example

Given f(x)=x3-8x2-4 What is f(2)?

The answer is '00'

summary

** Function evaluates to indeterminate value: ** Function f(x) evaluates to indeterminate value for x=a if f(a)=00.

Outline

The outline of material to learn "limits (calculus)" is as follows.

Note : * click here for detailed outline of Limits(Calculus).*

→ __Indeterminate and Undefined__

→ __Indeterminate value in Functions__

→ __Expected Value__

→ __Continuity__

→ __Definition by Limits__

→ __Geometrical Explanation for Limits__

→ __Limit with Numerator and Denominator__

→ __Limits of Ratios - Examples__

→ __L'hospital Rule__

→ __Examining a function__

→ __Algebra of Limits__

→ __Limit of a Polynomial__

→ __Limit of Ratio of Zeros__

→ __Limit of ratio of infinities__

→ __limit of Binomial__

→ __Limit of Non-algebraic Functions__