Calculus & Analysis Vocabulary

the instantaneous rate of change of a function

“The derivative of position with respect to time is velocity.”

Origin: Latin derivare `to draw off`, from de- + rivus `stream`

the accumulation of quantities, or the area under a curve

“The integral of velocity over time gives displacement.”

Origin: Latin integralis `making up a whole`, from integer `whole`

the value a function approaches as the input approaches some value

“The limit of 1/x as x approaches infinity is zero.”

Origin: Latin limes `boundary, frontier`

a line that a curve approaches but never touches

“The function has a horizontal asymptote at y = 0.”

Origin: Greek asymptotos `not falling together`, from a- `not` + syn `together` + ptotos `fallen`

the property of approaching a definite value or state

“The series 1 + 1/2 + 1/4 + ... converges to 2.”

Origin: Latin convergere `to incline together`, from con- + vergere `to bend`

the property of failing to approach any finite limit

“The harmonic series diverges to infinity.”

Origin: Latin divergere `to go in different directions`, from dis- + vergere `to bend`

having no breaks, jumps, or discontinuities

“A continuous function can be drawn without lifting the pen.”

Origin: Latin continuus `uninterrupted`, from continere `to hold together`

an infinitesimally small change in a variable

“The differential dx represents an infinitesimal change in x.”

Origin: Medieval Latin differentialis, from Latin differentia `difference`

a point where a curve changes from concave to convex or vice versa

“At the inflection point, the second derivative equals zero.”

Origin: Latin inflectere `to bend`, from in- + flectere `to bend`

a maximum or minimum value of a function

“Finding extrema is essential in optimization problems.”

Origin: Latin extremum `outermost point`, from exterus `outer`