4.6 De l'Hopital's rule for indefinite forms (1) For the following limits, first identify the indefinite form to which they give rise, then use de l'Hopital's rule to evaluate them, identifying which version of the rule you are using. In some cases, some manipulation is necessary to recast the original form into a or form. Note that more than one application of the rule is sometimes also required. (a) lim 1 - COST (b) lim -I- 3:12 1 - 22 (c) lim (d) lim cos(x - r-) - 1 T-1- arccos I arctan : (e) lim Inr (f) lim sin r -+1 tan (72) sin In (g) lim $40 1-4: (h*) lim 240 In (cosm) (i) lim sinha - sinc 1-e-x (i) lim 240 cosh : - cost (k) lim sinh (1 + x2) Vx - 1 (1* ) lim (1 + cos r) (tan ? ) TV + 2 (m*) lim (n) lim el/ Inr T-+00 (o* ) lim r arcsin(e ) T-+00 (p) lim In(x - 2) sin(mr) T-+2+ (q*) lim (x - v) tan () 24+1+' (r*) lim r arctanr - arccos T-+00