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
a) Step 1: Substitute x=2 into the expression. _x 2 (3-x)/(x+2) = (3-2)/(2+2) Step 2: Simplify the expression. (1)/(4) The limit is (1)/(4). b) Step 1: Substitute x=1 into the expression. _x 1 (5-x)/(x+3) = (5-1)/(1+3) Step 2: Simplify the expression. (4)/(4) = 1 The limit is 1. c) Step 1: Identify the highest power of x in the denominator, which is x. Divide both the numerator and the denominator by x. _x [3]x^3 - 3x + 23x+x^1/3+2 = _x [3]x^3 - 3x + 2x3x+x^1/3+2x Step 2: Rewrite the terms by moving x inside the cube root as x^3 and simplifying. _x ([3]x^3 - 3x + 2)/(x^3)(3x)/(x)+x^1/3x+(2)/(x) = _x ([3]1 - 3)/(x^2) + (2)/(x^3)3+(1)/(x^2/3)+(2)/(x) Step 3: Apply the limit. As x , terms like (c)/(x^n) approach 0. [3]1 - 0 + 03+0+0 = [3]13 = (1)/(3) The limit is (1)/(3). d) Step 1: Substitute x=1 into the expression. _x 1 (x^2-2)/(x^2-x-3) = (1^2-2)/(1^2-1-3) Step 2: Simplify the expression. (1-2)/(1-1-3) = (-1)/(-3) = (1)/(3) The limit is (1)/(3). Send me the next one 📸