L'Hospital's Rule

Definition

L'Hospital's Rule is a mathematical tool used to evaluate limits involving indeterminate forms such as 0/0 or ∞/∞. It states that if the limit of f(x)/g(x) as x approaches a certain value is an indeterminate form, then taking the derivative of both f(x) and g(x) and evaluating their ratio can help determine the limit.

Related terms

Indeterminate Form:

An indeterminate form refers to expressions that cannot be evaluated directly because they yield ambiguous results, such as 0/0 or ∞/∞. L'Hospital's Rule helps resolve these forms by applying differentiation techniques.

Limit Laws: Limit laws are rules that allow us to manipulate limits algebraically without evaluating them directly. These laws include properties such as sum/difference rule, product rule, quotient rule, etc., which aid in solving limits.

Taylor Series:

A Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of its derivatives at a single point. It can be used to approximate functions and evaluate limits.