limit as x goes to 0 of sin(x)/x
limit as x goes to 0 of (1-cos(x))/x
The limit of a function is...
the intended height
a limit does not exist when...
the function has a jump, asymptote, or oscillates.
If when the x values are approaching c from either side and f(x) becomes arbitrarily close to a single number, L,...
then the limit of f(x) as x approaches c is L
Composition properties of limits
limit as x approaches c of f(g(x) = f(lim g(x))
If lim f(x) = L ,then lim b×f(x) =
If lim f(x) = L and lim g(x) = K, then lim f(x)±g(x) =
L ± K
If lim f(x) = L and lim g(x) = K, then lim f(x)×g(x)=
If lim f(x) = L and lim g(x) = K, then lim f(x)/g(x) =
If lim f(x) = L, then lim f(x)ⁿ =
a limit in which f(x) increases or decreases without bound, as x approaches c
Does an infinite limit exist?
An infinite limit fails to exist since it never reaches a particular y value.