_ x 0 |x| |x|+x^2 =

Step-by-step solution

To evaluate the limit _ x 0 |x| |x| + x^2 , we consider left and right limits due to the absolute value. For x 0^+ where x > 0 and |x| = x , the expression becomes x x + x^2 . Canceling x gives 1 1 + x , which approaches 1 . For x 0^- where x Since both limits equal 1 , the limit exists and is 1 . The answer is B.