Using the L'Hospital's rule, determine the following limits.

(a)lim x1+ x^1/(1x)

(b)lim x0 (1 2x)^1/x

Find all asymptotes of the following rational functions.

(a) y = 2x^2 + x 1

______________

X^2 + x - 2

(b) y =x^3 x

____________

x^2 6x - 5

Using the L'Hospital's rule, determine the following limits:

(a) limx (1 + a/x)^bx

(b) limx (2x - 3/2x + 5 )^2x+1