limit

(noun)

a value to which a sequence or function converges

Related Terms

Examples of limit in the following topics:

  • The Lambda Limit

  • Limit of a Function

    • The notion of a limit has many applications in modern calculus.
    • In particular, the many definitions of continuity employ the limit: roughly, a function is continuous if all of its limits agree with the values of the function.
    • If both of these limits are equal to $L$ then this can be referred to as the limit of $f(x)$ at $p$.
    • A graph of the above function, demonstrating that the limit at $x_0$ does not exist.
    • The limit as the function approaches $x_0$ from the left does not equal the limit as the function approaches $x_0$ from the right, so the limit of the function at $x_0$ does not exist.

  • Student Learning Outcomes

  • Precise Definition of a Limit

    • The $(\varepsilon,\delta)$-definition of limit (the "epsilon-delta definition") is a formalization of the notion of limit.
    • The $(\varepsilon,\delta)$-definition of limit ("epsilon-delta definition of limit") is a formalization of the notion of limit.
    • The $(\varepsilon,\delta)$-definition of limit is a formalization of the notion of limit.
    • Therefore, the limit of this function at infinity exists.
    • Therefore, the limit of this function at infinity exists.

  • Calculating Limits Using the Limit Laws

    • Limits of functions can often be determined using simple laws, such as L'Hôpital's rule and squeeze theorem.
    • Limits of functions can often be determined using simple laws.
    • It is typically used to confirm the limit of a function via comparison with two other functions whose limits are known or easily computed.
    • Let $I$ be an interval having the point $a$ as a limit point.
    • Calculate a limit using simple laws, such as L'Hôpital's Rule or the squeeze theorem

  • Infinite Limits

    • Limits involving infinity can be formally defined using a slight variation of the $(\varepsilon, \delta)$-definition.
    • Limits involving infinity can be formally defined using a slight variation of the $(\varepsilon, \delta)$-definition.
    • If the degree of $p$ is less than the degree of $q$, the limit is $0$.
    • If the limit at infinity exists, it represents a horizontal asymptote at $y = L$.
    • Therefore, the limit of this function at infinity exists.

  • Congressional Terms and Term Limits

    • Term Limits, Inc. v.
    • Term Limits was the largest private organization pushing for Congressional term limits.
    • The term limits intended simultaneously to reform legislatures remain in fifteen states.
    • Sabato revived the debate over term limits by arguing in A More Perfect Constitution that the success and popularity of term limits at the state level suggests that they should be adopted at the federal level as well.
    • Summarize the attempts to impose term limits on Senators and Representatives

  • Finding Limits Algebraically

    • This set of rules is often called the algebraic limit theorem, expressed formally as follows:
    • In each case above, when the limits on the right do not exist (or, in the last case, when the limits in both the numerator and the denominator are zero), the limit on the left, called an indeterminate form, may nonetheless still exist—this depends on the functions f and g.
    • These rules are also valid for one-sided limits, for the case $p = \pm$, and also for infinite limits using the following rules:
    • The limit of $f(x)= \frac{-1}{(x+4)} + 4$ as $x$ goes to infinity can be segmented down into two parts: the limit of $\frac{−1}{(x+4)}$ and the limit of $4$.
    • Therefore, the limit of $f(x)$ as $x$ goes to infinity is $4$.

  • Limited Government

    • In a limited government, the power of government to intervene in the exercise of civil liberties is restricted by constitutional law.
    • The United States of America, a constitutionally limited republic, is an example of a constitutionally limited government.
    • The Constitution limits the power of the government in several ways.
    • Limited government exists where some effective limits restrict governmental power.
    • Describe the particular species of limited government operative in the United States' federal system.

  • Limiting Reagents

    • The reagent that limits how much product is produced (the reactant that runs out first) is known as the limiting reagent.
    • In a chemical reaction, the limiting reagent, or limiting reactant, is the substance that has been completely consumed when the chemical reaction is complete.
    • If the amount of B present is less than is required, then B is the limiting reagent.
    • Since there is only 0.28 mol C2H3Br3 present, C2H3Br3 is the limiting reagent.
    • The reactant that produces the least amount of product is the limiting reagent.