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# Indeterminate Form Calculus

TopIndeterminate form Calculus is an algebraic expression obtained in the form of limits. Limits that are involving algebraic operations are usually performed replacing sub-expressions by their limits. If the expression that is obtained after this substitution would not give enough information to calculate the original limit of the function this is known as intermediate form of calculus. The intermediate forms are 00, 0/0, 1,∞, -∞, ∞/∞, 0 * ∞ and ∞0.
The most general form of the intermediate form is 0/0. As the value of the variable x reaches to the zero, the value of the ratios x/x, x/x3, x2/x to infinity, one and zero respectively. In each case above stated if the values of the numerator and denominator are calculated and plugged into the division operation, the resulting expression would be zero/zero (0/0). The result of this 0/0 could be 0, infinity and 1. This is because the expression 0/0 is intermediate.
Two Functions f(x) and g(x) are approaches to zero as x approaches to some limit Point a is not enough to evaluate the limit
limx--> a f(x) / g(x)
The existence of the limit (might not exist, would diverge to infinity or would not converge) depends totally upon the functions f(x) and g(x). For some functions a value can be defined even at the points where the function is discontinuous like the function |x| / x is undefined for the value x = 0 in a real analysis.
It’s not necessary that every undefined algebraic expression is an intermediate form for example the expression 1 / 0 is undefined for the real Numbers but it not the intermediate form. This is because any limit that gives an increment to this form will diverge to infinity.
An intermediate form can be given sometimes in a numerical value like the value of the expression 00, is 1 when this represents an empty product.