Question

Find the limits: (i) lim[x→1] [(x²+1)/(x+100)] (ii) lim[x→2] [(x³-4x²+4x)/(x²-4)] (iii) lim[x→2] [(x²-4)/(x³-4x²+4x)] (iv) lim[x→2] [(x³-2x²)/(x²-5x+6)] (v) lim[x→1] [(x-2)/(x²-x) - 1/(x³-3x²+2x)]

Evaluate: (i) lim[x→1] (x¹⁵-1)/(x¹⁰-1) (ii) lim[x→0] (√(1+x)-1)/x