Use continuity to evaluate the limit. \[ \lim _{x \rightarrow 1} \frac{48+\sqrt{x}}{\sqrt{48+x}} \]

To evaluate the limit \[ \lim _{x \rightarrow 1} \frac{48+\sqrt{x}}{\sqrt{48+x}}, \] we can utilize the **continuity** of the functions involved. Both the numerator and the denominator are continuous at \( x = 1 \), meaning we can directly substitute \( x = 1 \) into the expression. Let's perform the substitution: \[ \frac{48 + \sqrt{1}}{\sqrt{48 + 1}} = \frac{48 + 1}{\sqrt{49}} = \frac{49}{7} = 7. \] Thus, the limit is: \[ 7 \] **Answer:** 7