Question

Could you please help with this problem?

Find the limit. Show all of your work. 2e*-! - X-1 (x - 1) (a) lim 50 X (6) lim 30 x x

Thanks

Answer 1

ay 22-1_2_ lim x 71 (x-1)3 This (8) forom so we can apply L? Hospital's sule we have = lim as he {20²1-2²-13 {(x-1)3} X > 1 d dx x-1 2 e = ling 2x .x > 1 3(x-1)2 Kl. X 2 im x 1 (x-12 This is also type so we also apply to tos pital's rule = lem al mare (ex-l_x) e ce {(x-1)"} 21

X-1 - 1 e Q 2 lim x7 q (x-1) This is again type apply L' Hospital's rule x+ X-!-,} d da {e e lim → 3 2 d (2-1) da 2-1 e eut ling X I 1 he' ouro ew/ Therefore ze*-|_x²_1 (x-1)3 lim eut xxl

50 b) lim x - 1 30 x 21 This tybe so we apply L2 Hospitals mule d dx es {x50_15 lim -- X-1 d 30 2 كم da -1} 50x 49 Z lim NI 30x 29 49-29 50 30 X lim X=1 11 5 5 lim X RI ni 20. X(12 10/