Calculus Examples

$lim_{x \to 0.5} x \ln (x)$

Step 1

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $0.5$ .

$lim_{x \to 0.5} x \cdot lim_{x \to 0.5} \ln (x)$

Step 2

Move the limit inside the logarithm.

$lim_{x \to 0.5} x \cdot \ln (lim_{x \to 0.5} x)$

Step 3

Evaluate the limits by plugging in $0.5$ for all occurrences of $x$ .

Tap for more steps...

Step 3.1

Evaluate the limit of $x$ by plugging in $0.5$ for $x$ .

$0.5 \cdot \ln (lim_{x \to 0.5} x)$

Step 3.2

Evaluate the limit of $x$ by plugging in $0.5$ for $x$ .

$0.5 \cdot \ln (0.5)$

Step 4

Multiply $0.5$ by $\ln (0.5)$ .

$- 0.34657359$