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
Here are the solutions to your limit problems. 1.) To evaluate the limit, substitute t=0 into the expression. Step 1: Substitute t=0 into the function. _t 0 (sqrt(1-t) + sqrt(1+t)) = sqrt(1-0) + sqrt(1+0) Step 2: Simplify the expression. = sqrt(1) + sqrt(1) = 1 + 1 = 2 The limit is: 2 2.) To evaluate the limit as t , divide every term in the numerator and denominator by the highest power of t in the denominator, which is t^2. Step 1: Divide all terms by t^2. _t (2t^2 + 3t + 1)/(t^2 - 1) = _t (2t^2)/(t^2) + (3t)/(t^2) + (1)/(t^2)(t^2)/(t^2) - (1)/(t^2) Step 2: Simplify the terms. = _t (2 + 3)/(t) + (1)/(t^2)1 - (1)/(t^2) Step 3: Apply the limit property _t (c)/(t^n) = 0 for n > 0. = (2 + 0 + 0)/(1 - 0) Step 4: Simplify the result. = (2)/(1) = 2 The limit is: 2 Send me the next one 📸