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Indeterminate form is a mathematical expression that can obtain any value depending on circumstances. In calculus , it is usually possible to compute the limit of the sum, difference, product, quotient or power of two functions by taking the corresponding combination of the separate limits of each respective function.
In mathematics, particularly in algebra, an indeterminate equation is an equation for which there is more than one solution. [1] For example, the equation a x + b y = c {\displaystyle ax+by=c} is a simple indeterminate equation, as is x 2 = 1 {\displaystyle x^{2}=1} .
In the second case, indeterminate generally indicates that a value or property can have many meaningful definitions. Additionally, it seems to be generally accepted that undefined values may not be safely used within a particular formal system, whereas indeterminate values might be, depending on the relevant rules of the particular formal ...
Here is a basic example involving the exponential function, which involves the indeterminate form 0 / 0 at x = 0: + = (+) = + = This is a more elaborate example involving 0 / 0 . Applying L'Hôpital's rule a single time still results in an indeterminate form.
Here both limits must converge to a finite value for the improper integral to be said to converge. This requirement avoids the ambiguous case of adding positive and negative infinities (i.e., the "" indeterminate form).
The exponent on an indeterminate in a term is called the degree of that indeterminate in that term; the degree of the term is the sum of the degrees of the indeterminates in that term, and the degree of a polynomial is the largest degree of any term with nonzero coefficient. [8]
When a partial fraction term has a single (i.e. unrepeated) binomial in the denominator, the numerator is a residue of the function defined by the input fraction. We calculate each respective numerator by (1) taking the root of the denominator (i.e. the value of x that makes the denominator zero) and (2) then substituting this root into the ...
In order to find the particular integral, we need to 'guess' its form, with some coefficients left as variables to be solved for. This takes the form of the first derivative of the complementary function. Below is a table of some typical functions and the solution to guess for them.