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Thought-Process to Discover Knowledge

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jogger,

exercise.

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exercise provides practice problems to become fluent in the concepts.

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summary of this topic

### Basics: Limit of a function

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Indeterminate Value in Functions

»  Functions evaluate to 0/0
→  eg: (x^2-4)/(x-2)|_(x=2) = 0/0

Though the function evaluates to 0/0, it may evaluate to a value.

### Indeterminate value in functions

plain and simple summary

nub

plain and simple summary

nub

dummy

Functions can evaluate to indeterminate value 0/0 at some input values.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Some functions evaluate to indeterminate value at some input values. This is illustrated with an example.

Keep tapping on the content to continue learning.
Starting on learning "indeterminate value in functions". ;; Some functions evaluate to indeterminate value at some input values. This is illustrated with an example.

What is the value of f(x) = color(deepskyblue)(x^2-1)/color(coral)(x-1) when x=2.2?

• 0/0
• indeterminate value
• 3.2

The answer is '3.2'. On substituting x=2.2, we get f(2.2)= color(deepskyblue)(2.2^2-1)/color(coral)(2.2-1).

What is the value of f(x) = color(deepskyblue)(x^2-1)/color(coral)(x-1) when x=1?

• 0/0
• indeterminate value
• both the above

The answer is 'Both the above'. On substituting x=1, we get
f(1)
quad quad =color(deepskyblue)(1^2-1)/color(coral)(1-1)
quad quad = color(deepskyblue)(0)/color(coral)(0).

Let us closely examine the function f(x) = color(deepskyblue)(x^2-1)/color(coral)(x-1). Can the numerator be factorized?

• Yes, x^2-1 = (x+1)(x-1)
• Cannot be factorized as Factorization is only for numbers, not for algebraic expressions

The answer is 'Yes - x^2-1 = (x+1)(x-1)'.

Rewriting the function f(x) = color(deepskyblue)(x^2-1)/color(coral)(x-1) as the function f(x) = color(deepskyblue)((x+1)(x-1))/color(coral)(x-1). Can the function be simplified?

• Simplified to f(x)= x+1
• Simplified only when x!=1 to f(x)= x+1

The answer is '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)
quad quad = x+1  when x!=1
quad quad = (x^2-1)/(x-1)  when x=1

By this it is concluded that f(x)|_(x=1) is indeterminate value 0/0.

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.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Function evaluates to indeterminate value: Function f(x) evaluates to indeterminate value for x=a if f(a) = 0/0.

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given f(x)=(x^3-8)/(x^2-4) What is f(2)?

• 0/0
• 10
• 1

The answer is '0/0'

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What is the value of f of x equals x squared minus 1 by x minus 1 when x equals 2 point 2?
0
0 by 0
indeterminate;value
indeterminate value
3;point;2;3.2
3 point 2
The answer is "3 point 2". On substituting x equals 2. point 2, we get f of 2 point 2 equals 2 point 2 squared minus 1 by 2 point 2 minus 1.
What is the value of f of x equals x squared minus 1 by x minus 1 when x equals 1?
0
0 by 0
indeterminate;value
indeterminate value
both;above
both the above
The answer is "Both the Above". On substituting x=1, we get ;; f of 1 ; equals 1 squared minus 1 by 1 minus 1 ;; equals 0 by 0.
Let us closely examine the function f of x equals x squared minus 1 by x minus 1. Can the numerator be factorized?
yes;s;squared;minus;1
yes; x squared minus 1 equals x plus 1 multiplied x minus 1
cannot;be;factorized;not;only
Cannot be factorized as Factorization is only for numbers, not for algebraic expressions
The answer is "Yes; x squared minus 1 equals x plus 1 multiplied x minus 1"
Rewriting the function f of x equals x squared minus 1 by x minus 1 as the function ;; f of x equals x + 1 multiplied x minus 1 divided by x minus 1. ;; Can the function be simplified?
simplified to; simplified 2
Simplified to f of x equals x + 1
only;when;not;equal;1
simplified only when x not equal 1 to f of x equals x + 1
The answer is "simplified only when x not equal 1 to f of x equals x + 1". Note that 0 cannot be canceled out in expressions or equations.
So the given function ;; f of x ;; equals x + 1 when x not equals 1 ;; and x squared minus 1 by x minus 1 when x equals 1 ;; By this it is concluded that f of x at x =1 is indeterminate value 0 by 0.;; Many students wrongly understand that the algebraic simplified, like canceling x minus 1 in the example above, solves the indeterminate value. It is not so, The function remains indeterminate at that input value x equals 1.
Functions can evaluate to indeterminate value 0/0 at some input values.
Function evaluates to indeterminate value: Function f of x evaluates to indeterminate value for x equals a if f of a equals 0 by 0.
Given f of x equal x cube minus 8 by x squared minus 4. What is f of 2?
0
0 by 0
10
10
1
1
The answer is "0 by 0"

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