please elaborate the answers with clarity and workings. studying for an exam. thanks

1. Determine the following limits:: (i) lim sin(14x) 7+0 sin (3x) (ii) lim y-+0 sin (9y) (iii) lim sin (3w) w-0 3w2+ 4w (iv) lim (sin(5m) cot(2m)) m+0 2. If g is a function such that (x + 1)2 2 9(x) 23(2x - 1) for all a 2 0. Determine lim, g(x). 3. Use the Squeeze Theorem to determine the following limits: (i) lim 512 - cos(3x) x2 + 10 (ii) lim 25 sin 4. Sketch the function f such that 12 -91 , if x # 13 fa) = 12 - 9 , if x = 13 Discuss (i) left and right continuity and (ii) continuity or discontinuity of the function f at x = 13