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.
function evaluating to 0/0
Consider the value of function f(x)=x2-1x-1 when x=1
On substituting x=1, we get
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
=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.
Given f(x)=x3-8x2-4 What is f(2)?
The answer is '00'
Function evaluates to indeterminate value: Function f(x) evaluates to indeterminate value for x=a if f(a)=00.
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
→ 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