What is the steps we need to do in order to solve those limits?

1. Limit [x->1] (x^4-x^3+x^2-3x+2) / (x^3-x^2-x+1) = 2

2. Limit [x-> PI/4] (1-tan^2(x)) / (sqrt(2)*cos(x)-1) = 4

3. Limit [x->PI/2] ( (2x+1) / (x) )^[e^[-x]] = (2+2/PI)^[(-e*PI)/(2)]

4. Limit [x->0] (sqrt(1+x)-x)^[1/x] = 1/sqrt(e)

5. Limit [x->1] (sqrt(x)+sqrt(x-1)-1) / (sqrt( (x^2)-1) ) = 1/sqrt(2)