1. The problem statement, all variables and given/known data 1. Lim x→0 Sin(x) * sqrt(1 + 1/x^2) Picture: https://i.gyazo.com/2f61c3c09d32447d4190fbdcd3f2f1e5.png 2. Limx→0 Sin(x)/sqrt(x^2 + x^3) Picture: https://i.gyazo.com/b50081d459ed61bcf1d4ae5baecfa7fa.png 2. Relevant equations 3. The attempt at a solution What I did with the first was turn it into: (sin(x)/x) * (x*sqrt(1 + 1/x^2) which results in (sin(x)/x) * (sqrt(x^2 + 1) The limit of that is 1 * sqrt(0+1) = 1*1 = 1 Is that correct? Doesn't the lim from right and left give different results? With the second one, I'm not sure what to do after: Sin(x) * (x^2 + x^3)^-1/2 If I multiply and divide by x I'll get 1 * 0/0 which is undefined, right?