Q. 50 - Calculus

Question

$\underset{x\to 0+}{\lim }\left(ln\left(1+\sqrt{x}\right)\right)$

Step-by-Step Solution

Answer

$\underset{x\to 0+}{\lim }\left(ln\left(1+\sqrt{x}\right)\right)=0$

Step 1. Given information

$\underset{x\to 0+}{\lim }\left(ln\left(1+\sqrt{x}\right)\right)$

Step 2. Plug in the values

$\underset{x\to 0+}{\lim }\left(ln\left(1+\sqrt{x}\right)\right)=\ln (1+\sqrt{x})$

$\underset{x\to 0+}{\lim }\left(ln\left(1+\sqrt{x}\right)\right)=\ln (1+\sqrt{0})$

$\underset{x\to 0+}{\lim }\left(ln\left(1+\sqrt{x}\right)\right)=0$