lim _(xarrow infty )(2x^2+6x-5)/(5x^2)-x-1

To find the limit of the given expression as approaches infinity, we can use the following steps:1. Divide both the numerator and denominator by the highest power of in the denominator.2. Simplify the expression.3. Evaluate the limit.Let's apply these steps to the given expression: Step 1: Divide both the numerator and denominator by : Step 2: Simplify the expression: As approaches infinity, the terms , , , and all approach 0. Therefore, the expression simplifies to: Step 3: Evaluate the limit: Therefore, the limit of the given expression as approaches infinity is .