1
Calculating Limits- HW Problems
1. Evaluate the following limits.
𝑥 2 +𝑥+1
𝑎. lim
𝑥→2 𝑥+1
𝑥 2 −5𝑥+6
𝑏. lim
𝑥→2 𝑥−2
𝑥 2 +4𝑥+3
𝑐. lim
𝑥→3 𝑥 2 +𝑥−6
𝑑. lim √𝑥 + 1
𝑥→3
(4+ℎ)2 −16
𝑒. lim
ℎ→0 ℎ
√4+ℎ−2
𝑓. lim
ℎ→0 ℎ
(√𝑥−1)
𝑔. lim
𝑥→1 𝑥−1
(√𝑥 2 +16−5)
ℎ. lim
𝑥→3 𝑥−3
1 1
+
𝑥 2
𝑖. lim
𝑥→−2 𝑥+2
2. Use the squeeze theorem to show:
𝑎. lim 𝑥 2 cos(2𝑥 ) = 0
𝑥→0
3
𝑏. lim 𝑥 sin ( ) = 0
𝑥→0 𝑥
Calculating Limits- HW Problems
1. Evaluate the following limits.
𝑥 2 +𝑥+1
𝑎. lim
𝑥→2 𝑥+1
𝑥 2 −5𝑥+6
𝑏. lim
𝑥→2 𝑥−2
𝑥 2 +4𝑥+3
𝑐. lim
𝑥→3 𝑥 2 +𝑥−6
𝑑. lim √𝑥 + 1
𝑥→3
(4+ℎ)2 −16
𝑒. lim
ℎ→0 ℎ
√4+ℎ−2
𝑓. lim
ℎ→0 ℎ
(√𝑥−1)
𝑔. lim
𝑥→1 𝑥−1
(√𝑥 2 +16−5)
ℎ. lim
𝑥→3 𝑥−3
1 1
+
𝑥 2
𝑖. lim
𝑥→−2 𝑥+2
2. Use the squeeze theorem to show:
𝑎. lim 𝑥 2 cos(2𝑥 ) = 0
𝑥→0
3
𝑏. lim 𝑥 sin ( ) = 0
𝑥→0 𝑥
