Compute
![\[ \lim_{x \to 4} \sqrt{1+\sqrt{x}}. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-f3b518fa7f293f2bc4142f6aef2b5e80_l3.png "Rendered by QuickLaTeX.com")
Since we know 
for 
is continuous and the composition of continuous functions is continuous, we know that the given function is continuous. Thus, the limit as 
is 
,
![\[ \lim_{x \to 4} \sqrt{1 + \sqrt{x}} = \sqrt{1+\sqrt{4}} = \sqrt{3}. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-95366a04d5ada8dc47e93df3e4130360_l3.png "Rendered by QuickLaTeX.com")
Compute
Since we know for is continuous and the composition of continuous functions is continuous, we know that the given function is continuous. Thus, the limit as is ,