Evaluate $\displaystyle \large \lim_{x \,\to\, 2}{\normalsize (x^3-5x+6)}$ by Direct substitution
The limit of a cubic function $x$ cube minus $5$ times $x$ plus $6$ should be evaluated in this limit problem by using direct substitution method as the value of $x$ approaches to $2$.
Evaluate the Limit by Direct substitution
So, directly substitute the variable $x$ by $2$ in the cubic function to find its limit by direct substitution when the value $x$ tends to $2$.
$\implies$ $\displaystyle \large \lim_{x \,\to\, 2}{\normalsize (x^3-5x+6)}$ $\,=\,$ $2^3-5(2)+6$
The limit of $x$ cube minus $5x$ plus $6$ as the value of $x$ closer to $2$ is expressed as an arithmetic expression.
Simplify the Arithmetic Expression
Now, it is time to simplify the arithmetic expression to find the limit of the given algebraic function.
$=\,\,$ $2 \times 2 \times 2 -5 \times 2+6$
$=\,\,$ $8-10+6$
$=\,\,$ $8+6-10$
$=\,\,$ $14-10$
$=\,\,$ $4$
Therefore, it is evaluated by using direct substitution that the limit of $x^3$ minus $5x$ plus $6$ as the value of $x$ approaches to $2$ is equal to $4$.