k(x) = \sqrt[5]{x}

If \lim_{x\rightarrow a^+}f(x) \neq \lim_{x\rightarrow a^-}f(x) then either f(a) = \lim_{x\rightarrow a^+}f(x) or f(a) = \lim_{x\rightarrow a^-}f(x) .

If \lim_{x\rightarrow a^+}f(x) = \lim_{x\rightarrow a^-}f(x) then \lim_{x\rightarrow a}f(x) = f(a).

If \lim_{x\rightarrow a}f(x) exists and is a real number then \lim_{x\rightarrow a^+}f(x) = \lim_{x\rightarrow a^-}f(x).

If \lim_{x\rightarrow a}f(x) exists then \lim_{x\rightarrow a}f(x) = f(a). 

If \lim_{x\rightarrow a}f(x) exists and is a real number then \lim_{x\rightarrow a^+}f(x) = \lim_{x\rightarrow a^-}f(x) provided the domain of the function includes values slightly greater than and slightly less than a.

If \lim_{x\rightarrow a^+}f(x) \neq \lim_{x\rightarrow a^-}f(x) then f(a) is undefined.

\lim_{x\rightarrow a}f(x) = f(a) provided the function f is defined when x=a.

If \lim_{x\rightarrow a^+}f(x) = \lim_{x\rightarrow a^-}f(x) then \lim_{x\rightarrow a}f(x) exists and is equal to the limit found by the one sided limits.

\lim_{x\rightarrow 2^+}f(x) = \dfrac{1}{4}

\lim_{x\rightarrow 2^+}f(x) = 4 

\lim_{x\rightarrow \infty}f(x) = \lim_{x\rightarrow -\infty}f(x) 

As x approaches zero, the function approaches a limit value L, where L \in \mathbb{R}.

\lim_{x\rightarrow 0}f(x) = 0 

\lim_{x\rightarrow 2}f(x) = \dfrac{1}{4}

The function value increases towards infinity as x approaches zero.

\lim_{x\rightarrow \infty} f(x) =0

\lim_{x\rightarrow 4} f(x) does not exist

\lim_{x\rightarrow 4^+} f(x) = -\infty

\lim_{x\rightarrow \infty} f(x) does not exist

\lim_{x\rightarrow 5^+} f(x) = 0 and \lim_{x\rightarrow 5^-} f(x) = 0 hence \lim_{x\rightarrow 5} f(x) = 0

\lim_{x\rightarrow -\infty} f(x) =0  

\lim_{x\rightarrow 4^+} f(x) = \infty

The derivative does not exist when h=0 as we cannot divide by zero.

If the function describes the distance of a particle from the origin after time t, then the instantaneous velocity at time t=b can be given by  \lim_{h\rightarrow 0} \dfrac{f(b+h)-f(b)}{h}.

The derivative of a function at the point (a, f(a)) is the gradient of the tangent line at that point.

If the function describes the distance of a particle from the origin after time t, then the instantaneous velocity at time t=b can be given by  \lim_{h\rightarrow 0} \dfrac{f(a+b)-f(a)}{h}.