Sketch the graph of the function y nbspradicx-1-1 stating

Question

1. (a) Sketch the graph of the function y = √(x-1)-1, stating the domain clearly.

(b) Determine whether the given function y = x(x² + 1/x²)/(x² - 2) is even, odd, or neither. Justify your answer.

(c) Give an example of a function that is even and odd.

(d) Find lim_{x→2 (}√(x² + 12) -4)/(x - 2)

(e) If, lim_x→2 f(x)/x² =1 find

(i) lim_x→2 f(x)
(ii) lim_x→2 f(x)/x

2. (a) Prove using ε and δ definition that lim_x→9 √(x -5) =2.

(b) Find lim_x→0 xsinx/2-2cosx

(c) Find lim_θ→0 θcot4θ/sin²θcot²2θ