Home » Blog » Evaluate the given limit

Evaluate the given limit

Compute

    \[ \lim_{x \to 4} \sqrt{1+\sqrt{x}}. \]


Since we know x^r for r \in \mathbb{Q} is continuous and the composition of continuous functions is continuous, we know that the given function is continuous. Thus, the limit as x \to 4 is f(4),

    \[ \lim_{x \to 4} \sqrt{1 + \sqrt{x}} = \sqrt{1+\sqrt{4}} = \sqrt{3}. \]

Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):