1
Infinite Limits-HW Problems
1. Find the following limits:
𝑥−1
𝑎. lim+
𝑥→3 𝑥−3
1
𝑏. lim (𝑥−3)2
𝑥→3
𝑥+2
𝑐. lim−
𝑥→2 𝑥 2 −4
1−𝑥
𝑑. lim−
𝑥→1 𝑥 2 −2𝑥+1
𝑥 2 −4
𝑒. lim+
𝑥→3 𝑥 2 +5𝑥+6
𝑥 2 −1
𝑓. lim
𝑥→−1+ 𝑥+1
𝑥
𝑔. lim −
𝑥→−3 𝑥 2 −9
2. Find the vertical asymptotes if they exist.
1
𝑎. 𝑓 (𝑥 ) =
𝑥 2 −9
𝑥 2 −𝑥
𝑏. 𝑔(𝑥 ) =
𝑥 3 −𝑥 2
𝑥 2 −𝑥−6
𝑐. ℎ(𝑥 ) =
𝑥 2 −4𝑥+3
Infinite Limits-HW Problems
1. Find the following limits:
𝑥−1
𝑎. lim+
𝑥→3 𝑥−3
1
𝑏. lim (𝑥−3)2
𝑥→3
𝑥+2
𝑐. lim−
𝑥→2 𝑥 2 −4
1−𝑥
𝑑. lim−
𝑥→1 𝑥 2 −2𝑥+1
𝑥 2 −4
𝑒. lim+
𝑥→3 𝑥 2 +5𝑥+6
𝑥 2 −1
𝑓. lim
𝑥→−1+ 𝑥+1
𝑥
𝑔. lim −
𝑥→−3 𝑥 2 −9
2. Find the vertical asymptotes if they exist.
1
𝑎. 𝑓 (𝑥 ) =
𝑥 2 −9
𝑥 2 −𝑥
𝑏. 𝑔(𝑥 ) =
𝑥 3 −𝑥 2
𝑥 2 −𝑥−6
𝑐. ℎ(𝑥 ) =
𝑥 2 −4𝑥+3
