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: Substitute x=2 into the expression to check for an indeterminate form. (2^2 + 3(2) - 10)/(2 - 2) = (4 + 6 - 10)/(0) = (0)/(0) Since this is an indeterminate form, we need to simplify the expression. Step 2: Factor the quadratic expression in the numerator. We need two numbers that multiply to -10 and add to 3. These numbers are 5 and -2. x^2 + 3x - 10 = (x+5)(x-2) Step 3: Rewrite the limit expression with the factored numerator. _x 2 ((x+5)(x-2))/(x-2) Step 4: Cancel out the common factor (x-2) from the numerator and denominator. This is valid because x 2 means x is approaching 2 but is not equal to 2, so x-2 ≠ 0. _x 2 (x+5) Step 5: Substitute x=2 into the simplified expression. 2+5 = 7 The final answer is 7. That's 2 down. 3 left today — send the next one.