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
Hey Victor, good to see you again. You're asking about the part where we evaluate the limit of the numerator as x . Let's break down that step: Step 1: Understanding the limit evaluation. We had the expression for N(x) as: N(x) = (2)/(sqrt(1+2)x)+(3)/(x^2) + sqrt(1+(3)/(x^2)) When we take the limit as x , we consider what happens to each term involving x: • For any constant c, _x (c)/(x) = 0. • For any constant c, _x (c)/(x^2) = 0. Applying this to our expression: • _x (2)/(x) = 0 • _x (3)/(x^2) = 0 (in the first square root) • _x (3)/(x^2) = 0 (in the second square root) So, when we substitute these limit values into the expression for N(x): _x N(x) = (2)/(sqrt(1+0+0) + 1+0) = (2)/(sqrt(1) + 1) = (2)/(1 + 1) = (2)/(2) = 1 This is how we arrive at the value of 1 for the limit of the numerator. Drop the next question!