Direct Substitution

Limits can be calculated by simply plugging in the value that the limit is approaching. This should be the first method of trying to solve a limit

Given $f (x) = 3 x^{2} + x + 4$ to find $lim_{x \to 3} f (x)$ you can simply substitute the value 3 into the function $f (x)$ .

\begin{aligned} lim_{x \to 3} 3 x^{2} + x + 4 & = 3 (3)^{2} + 3 + 4 \\ = 34 \end{aligned}