Calculus & Analysis Vocabulary

the instantaneous rate of change of a function

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

the accumulation of quantities, or the area under a curve

“The integral of velocity over time gives displacement.”

the value a function approaches as the input approaches some value

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

a line that a curve approaches but never touches

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

the property of approaching a definite value or state

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

the property of failing to approach any finite limit

“The harmonic series diverges to infinity.”

having no breaks, jumps, or discontinuities

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

an infinitesimally small change in a variable

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

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

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

a maximum or minimum value of a function

“Finding extrema is essential in optimization problems.”