Two questions I don't know how to solve...

Not sure how to approach these questions, math isn't my strongest subject ahah

1. 

(Limits, by any means necessary. ) Several limits are listed below. Using literally any techniques you like ("intuitive" limit techniques, limit laws, visual intuition, plugging in values, consulting the Oracle of Delphi, etc), find each limit if it exists or state that it does not exist. (a) lim In(In(In(In(In(a))))) I-+00 (e) lim T-+2 (b) lim sin(x) - sin(x) cos? (x) lim sin?(x) - 4 sin() + 3 23 (f) T-+1/2 sin(x) - 1 7-6 - 1 (c) lim -1x-1 (g) lim In(x2 + 1) (d) lim sin (ex - cos(x) + In(x2 + 1)) (h) lim x3 - 2x + In(x - 1) sin(x) T-+2+ ref cos( TX)(Statements about limits.) Three statements are given below. Determine which statements are true and which are false. Prove the true statements, and disprove the false statements by giving examples with justication. (a) Let a. 6 1R. Suppose that g : IR >- R are two functions with the property that lim f(:c),al:i_r.nig(x) both do not exist. Then in}; (f(:c) +g(9:)) also does not exist. 3}8 (b) Suppose that f, g : R > R both do not have any horizontal asymptotes. Then the product of f and g, denoted f ' 9, also does not have any horizontal asymptotes (c) If f : R > R, then there is at least one real number a. E R such that lim f(:c) exists. iii-+6