What is an indeterminate answer?
An undefined expression involving some operation between two quantities is called an indeterminate form if it does not evaluate to a single number value or infinity.
An indeterminate form occurs when determining the limit of the ratio of two functions, such as x/x^3, x/x, and x^2/x when x approaches 0, the ratios go to ∞, 1, and 0 respectively.
So, L'Hospital's Rule tells us that if we have an indeterminate form 0/0 or ∞/∞ all we need to do is differentiate the numerator and differentiate the denominator and then take the limit.
The expressions 0⋅∞,∞−∞,1∞,∞0, and 00 are all considered indeterminate forms. These expressions are not real numbers. Rather, they represent forms that arise when trying to evaluate certain limits.
S1:limx→0−[x]x is an indeterminate from (where [.] denotes greatest integer function).
According to some Calculus textbooks, 0^0 is an ``indeterminate form''. When evaluating a limit of the form 0^0, then you need to know that limits of that form are called ``indeterminate forms'', and that you need to use a special technique such as L'Hopital's rule to evaluate them.
He got his wish with an indeterminate sentence. He got an indeterminate sentence, with a minimum six years. There were two types of indeterminate sentence: life imprisonment and imprisonment for public protection. He got an indeterminate sentence and must serve at least nine months.
1/∞ is not an indeterminate form, it is 1/∞ = 0. ∞/1 is not an indeterminate form, but ∞/1 = ∞.
adjective. not determinate; not precisely fixed in extent; indefinite; uncertain. not clear; vague. not established. not settled or decided.
This is known as an indeterminate form, because it is unknown. One to the power infinity is unknown because infinity itself is endless.
Why is zero * infinity indeterminate?
Zero is so small that it makes everyone vanish, but infinite is so huge that it makes everyone infinite after multiplication. In particular, infinity is the same thing as "1 over 0", so "zero times infinity" is the same thing as "zero over zero", which is an indeterminate form.
It is generally indeterminate because it can take on many values. For example we know two basic facts from exponent rules over real numbers: for positive real because by the basic definition of exponentiation this expression is equal to 0 times itself times which is 0 no matter how many times you do it.
An intermediate source form is an internal form of a program created by the compiler while translating the program from a high-level language to assembly-level or machine-level code. There are a number of advantages to using intermediate source forms.
An indeterminate structure is a structure that is also stable, but It has more unknown forces than the total number of available equilibrium equations. For analyzing an indeterminate structure, compatibility equations are required along with the equilibrium equations.
Product: ∞ ⋅ ∞ \infty \cdot \infty ∞⋅∞ is not indeterminate; the limit is ∞ \infty ∞.
Another states that infinity/0 is one of the indeterminate forms having a large range of different values. The last reasons that infinity/0 "is" equal to infinity, ie: Suppose you set x=0/0 and then multiply both sides by 0. Then (0 x)=0 is true for most any x-- indeterminant.
These convert the indeterminate form to one that we can solve. The two formulae are the following: If lim x → + ∞ f ( x ) = 1 and lim x → + ∞ g ( x ) = ± ∞ then, lim x → + ∞ f ( x ) g ( x ) = e ( lim x → + ∞ ( f ( x ) − 1 ) ⋅ g ( X ) )
indeterminate sentence, in law, term of imprisonment with no definite duration within a prescribed maximum. Eligibility for parole is determined by the parole authority.
In short, this Rule tells us that in case we are having indeterminate forms like 0/0 and ∞/∞ then we just differentiate the numerator as well as the denominator and simplify evaluation of limits.
In ordinary arithmetic, the expression has no meaning, as there is no number which, multiplied by 0, gives a (assuming a≠0), and so division by zero is undefined. Since any number multiplied by zero is zero, the expression 0/0 also has no defined value; when it is the form of a limit, it is an indeterminate form.
What is difference between indeterminate and indeterminate?
Determinate varieties require little or no staking of the plant. Indeterminate varieties develop into vines that never top off and continue producing until killed by frost. They are preferred by home growers and local-market farmers who want ripe fruit throughout the season.
. If you add one to infinity, you still have infinity; you don't have a bigger number. If you believe that, then infinity is not a number.
Yet even this relatively modest version of infinity has many bizarre properties, including being so vast that it remains the same, no matter how big a number is added to it (including another infinity). So infinity plus one is still infinity.
Any number times 0 is 0. So, the answer is undefined.
In ordinary arithmetic, the expression has no meaning, as there is no number that, when multiplied by 0, gives a (assuming ); thus, division by zero is undefined. Since any number multiplied by zero is zero, the expression is also undefined; when it is the form of a limit, it is an indeterminate form.
When Can You Use L'hopital's Rule. We can apply L'Hopital's rule, also commonly spelled L'Hospital's rule, whenever direct substitution of a limit yields an indeterminate form. This means that the limit of a quotient of functions (i.e., an algebraic fraction) is equal to the limit of their derivatives.
Using L Hospital's rule, we can solve the problem in 0/0, ∞/∞, ∞ – ∞, 0 x ∞, 1∞, ∞0, or 00 forms. These forms are known as indeterminate forms.
Hence ∞/∞ cannot be determined. Same with 0/0 - it doesn't mean anything, hence indeterminate. You cannot determine what such a number is. Now, ∞∗0 also is meaningless, since anything times infinity is infinity and anything times 0 is 0, so infinity times zero cannot be determined.
Forms that are not Indeterminate
Quotient: The fractions 0 ∞ \frac0{\infty} ∞0 and 1 ∞ \frac1{\infty} ∞1 are not indeterminate; the limit is 0 0 0. The fractions 1 0 \frac10 01 and ∞ 0 \frac{\infty}0 0∞ are not indeterminate.
Limits Without Using L'Hospital's Rule:
L'Hospital's rule tells us that if we have an indeterminate form, what we need to do is to take the derivative of the numerator and take the derivative of the denominator so that the function we are taking limits will no longer be indeterminate before we take the actual limit.
Is 0 0 is infinity or indeterminate form?
If you are dealing with limits, then 00 is an indeterminate form, but if you are dealing with ordinary algebra, then 00 = 1.
Any number times any number is a number, so let's just call any number 1. Any number times 0 equals 0 and any number times infinity equals infinity. In this way, they are similar to the square root of -1. As long as there are an even number, you get a real number.