ejercicios y problemas sobre limites infinitos

1. COLEGIO REMBRANDT
TALLER SOBRE LÍMITES II - GRADO ONCE
PROFESOR: RICARDO REGINO A.
ALUMNO: _____________________________________________________ CURSO: ______________
LÍMITES TRIGONOMÉTRICOS
1. lim
x→0
Sen4x
x
R/ = 4
2. lim
x→0
1−Cosx
x2 R/ =
1
2
3. lim
x→0
Sen 5x
2x
R/ =
5
2
4. lim
x→0
Sen3x
Sen5x
R/ =
3
5
5. lim
x→0
x−Sen3x
x+Sen2x
R/ = −
1
2
6. lim
x→0
Tgx−Senx
x3 R/ =
1
2
7. lim
𝑥→
𝜋
4
1−𝐶𝑡𝑔𝑥
1−𝑇𝑔𝑥
R/ = −1
8. lim
𝑥→0
1−𝐶𝑜𝑠3
𝑥
𝑆𝑒𝑛2 𝑥
R/ =
3
2
9. lim
𝑥→
𝜋
4
𝑆𝑒𝑛𝑥−𝐶𝑜𝑠𝑥
1−𝑇𝑔𝑥
R/= −
√2
2
10. lim
x→
𝜋
3
Sen3x
1−2Cosx
R/ = −√3
11. lim
𝑥→
𝜋
6
2𝑆𝑒𝑛2
𝑥+𝑆𝑒𝑛𝑥−1
2𝑆𝑒𝑛2 𝑥−3𝑆𝑒𝑛𝑥+1
R/ = −3
12. lim
𝑥→
𝜋
4
𝑆𝑒𝑛2𝑥−𝐶𝑜𝑠2𝑥−1
𝐶𝑜𝑠𝑥−𝑆𝑒𝑛𝑥
R/ = −√2
13. lim
𝑥→0
1−𝐶𝑜𝑠2𝑥
𝑥𝑆𝑒𝑛𝑥
R/ = 2
14. lim
𝑥→0
𝐶𝑜𝑠2𝑥
𝐶𝑜𝑠𝑥−𝑆𝑒𝑛𝑥
R/ = √2
15. lim
𝑥→0
√1+𝑇𝑔𝑥−√1+𝑆𝑒𝑛𝑥
𝑥3
R/ =
1
4
LIMITES AL INFINITO
1. lim
𝑥→∞
2 𝑥+1
+3 𝑥+1
2 𝑥+3 𝑥
R/= 3
2. lim
𝑥→∞
( 𝑥 − √𝑥2 − 4)
R/= 0
3. lim
𝑥→∞
√𝑥4 + 5𝑥2 + 6 − 𝑥2
R/= 5/2
4. lim
𝑥→∞
(√𝑥4
− 4𝑥2
− 2 − (𝑥2
− 1))
R/= -1
5. lim
𝑥→∞
𝑥3
−3𝑥2
+𝑥
𝑥−2
R/= ∞
6. lim
𝑥→−∞
𝑥2
−𝑥
4𝑥3+5𝑥2+1
R/= 0
7. lim
𝑥→−∞
√𝑥2
−2𝑥+3
𝑥+3
R/= 1
8. lim
𝑥→−∞
𝑥3
√𝑥6+4
R/= -1
9. lim
𝑥→−∞
𝑥4
−3𝑥2
+𝑥
5𝑥4+3𝑥3−2𝑥+1
R/= 1/5
10. lim
𝑥→∞
𝑥4
−3𝑥2
+4
𝑥5+2𝑥3−𝑥+1
R/= 0
11. lim
𝑥→∞
2𝑥−3
𝑥+1
R/= 2
12. lim
𝑥→∞
√𝑥2 − 9 − √𝑥2 − 1
R/= 0
13. lim
𝑥→∞
√𝑥3 − 1
3
− 𝑥
R/= 0
14. lim
𝑥→∞
3𝑥4
+𝑥3
−2𝑥−4
𝑥2−𝑥+1
R/= ∞
15. lim
𝑥→∞
√𝑥3 − 2𝑥23
− √𝑥3 − 5
3
R/= -2/3