Determine the one-sided limits numerically or graphically. If infinite, state whether the one-sided limits are oo or -oo, and describe the corresponding vertical asymptote. limx→1±x5+x−2x2+x−2

Question

Determine the one-sided limits numerically or graphically. If infinite, state whether the one-sided limits are oo or -oo, and describe the corresponding vertical asymptote.  limx→1±x5+x−2x2+x−2

Roosevelt Houghton · Accepted Answer

Given  limx→1x5+x−2x2+x−2  To find: One sided limit.  Vertical asymptotes.  Given that limx→1x5+x−2x2+x−2  Now the equation x5+x−2 can be factored as (x−1)(x4+x3+x2+x+2)  and the equation x2+x−2 can be factored as (x+2)(x−1).  So,  limx→1x5+x−2x2+x−2=limx→1(x−1)(x4+x3+x2+x+2)(x−1)(x+2)  Cancel out the term (x-1) from numerator and denomiantor,  limx→1x5+x−2x2+x−2=limx→1(x4+x3+x2+x+2)(x+2)  =(14+13+12+1+2}{1+2}  =63  =2  Therefore,  limx→1x5+x−2x2+x−2=2  Now to find vertical asymptotes,  The line x=a is called vertical asymptote of the curve y=f(x) if limx→af(x)=±∞  For x=-2  limx→−2x5+x−2x2+x−2=limx→−2(−2)5+(−2)−2(−2)2+(−2)−2  =limx→−2−32−44−2−2  =∞  Therefore x=-2 is vertical asymptote  Therefore,  limx→1x5+x−2x2+x−2=2  The vertical asymptote is at x=-2

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Determine the one-sided limits numerically or graphically. If infinite, state wh

Answered question

Answer & Explanation

New Questions in Calculus 1