Matheno - Learn Well and Excel

Limits – Substitution

This is the first thing you should always try: just plug the value of x into f(x). If you obtain a number (and in particular, if you don’t get  $\dfrac{0}{0}$), you have your answer and are finished. In that case, these problems are completely straightforward.


Find $\displaystyle{\lim_{x \to 2}(x^3-5x + 7)}$.


\begin{align*} \lim_{x \to 2}(x^3-5x + 7) &= (2)^3 -5(2) + 7 \\ &= 8 -10 + 7 = 5 \quad \cmark \end{align*}

Practice this (simple!) tactic in the next few problems. The solutions are immediately available using the Show/Hide Solution toggle. #5 illustrates an important point.