Method: Squeeze Theorem

Step 1: Try Option 1: Plug It In

Step 2: Confirm that you have three equations that fit the Squeeze Theorem Inequality, $\mathit{g}\mathit{\left(}\mathit{x}\mathit{\right)}\mathit{\le }\mathit{f}\mathit{\left(}\mathit{x}\mathit{\right)}\mathit{\le }\mathit{h}\mathit{\left(}\mathit{x}\mathit{\right)}$.

Step 3: Apply the limit portion of the Squeeze Theorem at the given x-value = c , to the outside equations to confirm $\underset{x\to c}{\lim }\mathit{ }\mathit{g}\mathit{\left(}\mathit{x}\mathit{\right)}\mathit{=}\underset{x\to c}{\lim }\mathit{ }\mathit{h}\mathit{\left(}\mathit{x}\mathit{\right)}\mathit{=}\mathit{L}$.

Step 4: Apply the conclusion of the Squeeze Theorem to answer the limit question about the equation in the middle, $\underset{x\to c}{\lim }\mathit{ }\mathit{f}\mathit{\left(}\mathit{x}\mathit{\right)}\mathit{=}\mathit{L}$.