ejercicios propuestos de limites. Matematica I

1. Rosalys Herrera 20.348.002
1. Lim 𝑦 → −1 (
𝑦2−2𝑦+2
𝑦−4
+ 1)
=(
(−1)2−2(−1)+2
−1−4
+ 1)
= (
1+2+2
−5
+ 1)
= (
5
−5
)
= (−1 + 1)
= 0
2. lim 𝑥 ⟶ 9
1
√ 𝑥
−
1
3
𝑥−9
=
1
√9
−
1
3
9−9
=
1
√9
−
1
3
0
=
1
3
−
1
3
0
=
0
0
= +∞

2. 3. lim 𝑇 ⟶ 2 (
𝑇2−6𝑇+8
𝑇2−5𝑇+6
)
𝑇−2
√𝑇−√2
= (
22−6(2)+8
22−5(2)+6
)
2−2
√2−√2
= (
4−12+8
4+10+6
)
0
0
= (0
0
)+∞
= (+∞)+∞
= +∞
4. lim 𝑘 ⟶ 6
2−√𝐾−2
𝐾2−36
=
2−√6−2
62−36
=
2−2
36−36
= +∞
5. lim 𝑥 ⟶
𝜋
4
𝑠𝑒𝑛 𝑥−cos 𝑥
1−tan 𝑥
=
𝑠𝑒𝑛(
𝜋
4
)−cos(
𝜋
4
)
1−tan(
𝜋
4
)
=
0,01370−0,9999
0,9862
= -1
6. lim ℎ ⟶ 0
(ℎ+3)2−9
ℎ
=
(0+3)2−9
0
= +∞
7. lim 𝑥 ⟶ ∞
6𝑥
√𝑥2+1
=
6(∞)
√∞2+1
=
∞
∞
= ∞