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
To go from the first expression to the second, we simplify the term inside the parenthesis in the numerator. Step 1: Focus on the expression inside the parenthesis: ( (1)/((2x)) - 1 ) Step 2: To subtract 1 from (1)/((2x)), we need a common denominator. We can rewrite 1 as ((2x))/((2x)). (1)/((2x)) - ((2x))/((2x)) Step 3: Now that they have a common denominator, we can combine the numerators: (1 - (2x))/((2x)) Step 4: Substitute this simplified expression back into the limit. The original expression was: _x 0 ((2x) ( 1)/((2x)) - 1 )x^3 Replacing the parenthesis with the simplified form: _x 0 ((2x) ( 1 - (2x))/((2x)) )x^3 Step 5: Multiply the terms in the numerator. The (2x) from the simplified parenthesis term moves to the denominator of the entire fraction: _x 0 ((2x) (1 - (2x)))/(x^3 (2x)) This is the step shown in your image. 3 done, 2 left today. You're making progress.