Question

1. (25 points) Evaluate the limit, if it exists. lim (x3 + 3x² 3 1+ 4x2 + 3.14) 2+1 (b) lim 29- - 9 x² - x - 20 (c) lim 1- -5 5

Answer 1

Answer is given below:

1. Ans=(1/4)
2. Ans=-infinity
3. Ans=1

solution: @ lim (x²+3x2 1 +4x²+3x4 -> lim ( x? (X+3) ) +x² (4+3x²) | Stepos Apply the quotient law : - lis, (x3 + 3x²) 2 lim (1+4x²+3x4) ² step now apply the sum law and constant multiple law - x = ( lim x² + 3 lim x ²2 (ity lim x² +3 lim x") 2. HI Steph. again, apply power law a = (lisay?+ 3 (lir, x))? (itu (in %+ (lim 92 steporvoo, of by basie Limit lacos f simplity Now, asic limit to (+372 (+40+303972 = (1 +4+3) 16 by 69 2020-2-20

xsa Step : Draw graph of (urg) - x x=9 gt has assymptotes at step ④: let x=(9 h) so that when x tg, so - lima & lim da xsa (-a) no (9-4-9) lim x-1 lisen -- ho tones = lehenengo toh - - 20 © in lim x-5 x²-x-20 x-5 step factorize the numerator lim x²–5x+4 x -20 nas (2-5) - lim ( 15 (x-4) - nas (as) = lim (2-4) xes = (5-4) = 1 2020-2-20