Limit

How it is used

The basic idea behind derivatives and integrals. 'lim x→0 sin x / x = 1' is read 'the limit as x approaches zero of sine x over x equals one'. A limit may exist, fail to exist or be infinite. Definite integrals also have upper and lower limits.

Example sentences

1. Find the limit as x approaches 2 of (x² − 4)/(x − 2).

2. The limit doesn't exist because the left-hand and right-hand limits are different.

Common collocations

• the limit as x approaches
• find the limit
• left-hand limit
• the limit does not exist
• take the limit

Related terms

• derivativeA function that gives the rate of change of another function at each point, which is the slope of its graph there; the derivative of x² is 2x.
• continuousHaving no breaks, jumps or holes; a function is continuous at a point if its limit there equals its value, so its graph can be drawn without lifting the pen.
• integralThe result of integration: either a family of functions whose derivative is the given function, or a number giving the area under a curve between two limits.
• functionA rule that takes each input from a set and gives exactly one output, for example f(x) = 2x + 1, which doubles a number and adds one.

More terms: Calculus

• differentiate
• integrate
• chain rule