Let $f(x)=\frac{x}{ln(x)}$

$($a$)$ Find each of the following limits$.($If the limit is infinite, enter $\text{'}\text{'}$ or $\text{'}-{}^{\text{'}}\text{'},$ as appropriate. If the limit does not otherwise exist, enter DNE.$)$

$($i$)\underset{x{0}^{+}}{lim}f(x)$

$($ii$)\underset{x{1}^{-}}{lim}f(x)$

$($iii$)\underset{x{1}^{+}}{lim}f(x)$

$($b$)$ Use a table of values to estimate $\underset{x}{lim}f(x).($If the limit is infinite, enter $\text{'}\text{'}$ or $\text{'}-\text{'},$ as appropriate. If the limit does not otherwise exist, enter DNE.$)$

A tank contains $1,000L$ of pure water. Brine that contains $10$ g of salt per liter of water is pumped into the tank at a rate of $25\frac{L}{m}in.$

$($a$)$ Find the concentration of salt after $t$ minutes $($in $\frac{g}{L}).$

$C(t)=,|\frac{g}{L}||$

$($b$)$ What happens to the concentration $($in $\frac{g}{L})$ as $t?$

$$ g$/$L

Need Help? $$

$$