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Contains terms and concepts from Calculus: Concepts and Applications by Paul A. Foerster as taught by Colin Suehring at McFarland High School
indeterminate form
0/0 or infinity/infinity
limit
the value that a function approaches as the input approaches some value
removable discontinuity
a characteristic of a function in which the function is continuous everywhere except for a hole at x=c
asymptote
a line that continually approaches a given curve but does not meet it at any finite distance
step discontinuity
if f(x) approaches different numbers from the right and from the left as x approaches c, then there is a step discontinuity at x=c
limit of a product
the product of the limit of each function
limit of a sum
the sum of the limits
limit of a quotient
quotient of limits
limit of a constant
the constant times the limit
limity of the identity function (limit of x)
limit of x as x approaches c = c
limit of a constant function
that constant
continuity at a point
function f is continuous at x=c if and only if
f(c ) exists
lim x—> c exists
if f(c ) = lim x—> c
continuity on an interval
function f is continuous on an interval of x-values if and only if it is continuous at each value of x in that interval
cusp
the point on the graph at which the function is continuous but the derivative is discontinuous, an abrupt change in direction or sharp point
one-sided limit
a limit that differs depending whether it is approached from left (x-->c-) or from right (x-->+)
if lim x→a⁺ f(x) ≠ lim x→a⁻ f(x) then
lim x→a f(x) does not exist
the limit does not exist and graph forms an asymptote when
lim f(x) as x approaches c -= +/- ∞
f(x) = c is a horizontal asymptote when
lim f(x) as x approaches +/- ∞ = c
the limit does not exist when
lim f(x) as x approaches +/- ∞ = +/- ∞
f(x) = c is a vertical asymptote when
lim |f(x)| as x approaches c = ∞
the intermediate value theorem
If function f is continuous for all x in the closed interval [a,b], and y is a number between f(a) and f(b), then there is a number x=c in (a,b) for which f(c)=y
Note 
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