Evaluate $\displaystyle \large \lim_{x \,\to\, 2}{\normalsize (x^3-5x+6)}$ by Direct substitution

Find $\displaystyle \large \lim_{x \,\to\, 2}{\normalsize (x^3-5x+6)}$

Substitute $x \,=\, 2$ in the cubic function

$=\,\,\,$ $2^3-5(2)+6$

$=\,\,\,$ $8-5 \times 2+6$

$=\,\,\,$ $8-10+6$

$=\,\,\,$ $8+6-10$

$=\,\,\,$ $14-10$

$=\,\,\,$ $4$

Therefore, the limit of $x^3-5x+6$ as $x$ is closer to $2$ is equal to $4$.

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