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Ejercicios limites
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 = ∞ ∞ = ∞
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