Please briefly give me explanations for these problems I have been struggled:

18. Find y'. You do not have to simplify your answer. sec2 x (a) y = log2(tan x) + (x2 + 3) /3. Answer: y' = 2x tan x In 2 + 3(2 2 + 3) 2/3 (b) y = + cos x + 3 cot x2 1+x (2" In(2)6x5 - sin x - 6x csc2(x2) ) (1 + x) - (2"- + cos x + 3 cot x2) Answer: y' = (1 + 20 ) 211. Evaluate the following limits, if they exist. (Do not use L'Hospital rule) Mm+1-%K? (a) 131) m _ 2 Answer: 0 1/ 2 _ 1/ (b) lim M Answer: 1/ 2 rHl h+32 (g) lim(28 + x2)ecos( 271 Answer: 0 using the squeeze theorem x-0 (h) lim sin (In a) Answer: 0 using the squeeze theorem xx->0+ In x5. Determine if the following functions are one-to-one, even, odd, periodic. Determine the intervals of increase / decrease. (a) f(x) = x2-10x+1 Answer: Not one-to-one, Neither even nor odd, not periodic, interval of decrease: (-0o, 5), interval of increase: (5, co) (b) f(x) = - sin 2x, x E (-T, T) Answer: Not one-to-one, not even, odd, not peri- odic, interval of increase: (- 4) 4 ), interval of decrease: (-TT, -4); (c) f(a) = In(2x - 2) - 5 Answer: one-to-one, neither even nor odd, not periodic, interval of increase: (1, co)7. Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and applying the appropriate transformations. (a)y=\\/23:+42 (b)y=ew_2+1