This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the highest power of x in the denominator. The given expression is a rational function. To evaluate the limit as x , we divide every term in the numerator and the denominator by the highest power of x in the denominator. The denominator is 2x^2 + 5x + 1, and its highest power of x is x^2. Step 2: Divide each term by x^2. _x ((3x^5)/(x^2) - (9x)/(x^2) + (2)/(x^2)(2x^2)/(x^2) + (5x)/(x^2) + (1)/(x^2)) Step 3: Simplify the expression. _x ((3x^3 - 9)/(x) + (2)/(x^2)2 + (5)/(x) + (1)/(x^2)) Step 4: Evaluate the limit by substituting x . As x , terms of the form (c)/(x^n) (where c is a constant and n > 0) approach 0. (3()^3 - 0 + 0)/(2 + 0 + 0) ()/(2) That's 2 down. 3 left today — send the next one.