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
Fresh day Victor, let's solve. 5. Evaluate: Part 1: _x 0^+ |x| Step 1: For x > 0, the absolute value |x| is equal to x. _x 0^+ |x| = _x 0^+ x Step 2: Substitute x=0 into the expression. _x 0^+ x = 0 The limit is 0. Part 2: _x 0^- |x| Step 1: For x < 0, the absolute value |x| is equal to -x. _x 0^- |x| = _x 0^- (-x) Step 2: Substitute x=0 into the expression. _x 0^- (-x) = -(0) = 0 The limit is 0. 6. Evaluate: Part 1: _x 2^+ |x - 2| Step 1: For x > 2, the expression x - 2 is positive, so |x - 2| = x - 2. _x 2^+ |x - 2| = _x 2^+ (x - 2) Step 2: Substitute x=2 into the expression. _x 2^+ (x - 2) = 2 - 2 = 0 The limit is 0. Part 2: _x 2^- |x - 2| Step 1: For x < 2, the expression x - 2 is negative, so |x - 2| = -(x - 2). _x 2^- |x - 2| = _x 2^- -(x - 2) Step 2: Substitute x=2 into the expression. _x 2^- -(x - 2) = -(2 - 2) = -(0) = 0 The limit is 0. 7. Evaluate: Part 1: _x 0^+ (|x|)/(x) Step 1: For x > 0, the absolute value |x| is equal to x. _x 0^+ (|x|)/(x) = _x 0^+ (x)/(x) Step 2: Simplify the expression. _x 0^+ (x)/(x) = _x 0^+ 1 Step 3: The limit of a constant is the constant itself. _x 0^+ 1 = 1 The limit is 1. Part 2: _x 0^- (|x|)/(x) Step 1: For x < 0, the absolute value |x| is equal to -x. _x 0^- (|x|)/(x) = _x 0^- (-x)/(x) Step 2: Simplify the expression. _x 0^- (-x)/(x) = _x 0^- (-1) Step 3: The limit of a constant is the constant itself. _x 0^- (-1) = -1 The limit is -1. Send me the next one 📸