Cálculo Diferencial Trabajo 2.docx

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1) lim

𝑥→0

√9+𝑥−3 𝑥

Aplicamos el límite.

√9 + 0 − 3 𝑥→0 0 lim

3−3 𝑥→0 0 lim

0 𝑖𝑛𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑐𝑖𝑜𝑛. 𝑥→0 0 lim

Aplicamos la racionalización o conjugación. √9 + 𝑥 − 3 √9 + 𝑥 + 3 ∗ 𝑥→0 𝑥 √9 + 𝑥 + 3 lim

lim

𝑥→0

(√9 + 𝑥)2 − (3)2 𝑥(√9 + 𝑥 + 3)

Aplicamos las potencias. lim

(9 + 𝑥) − 9

𝑥→0 𝑥(√9

+ 𝑥 + 3)

9 – 9=0 lim

𝑥

𝑥→0 𝑥(√9

+ 𝑥 + 3)

X en el numerador y en el denominador se cancelan, quedando 1 en el numerador. lim

𝑥→0 (√9

1 + 𝑥 + 3)

Aplicamos nuevamente el límite. lim

𝑥→0 (√9

1 + 0 + 3)

1 1 = 𝑥→0 3 + 3 6 lim

√9 + 𝑥 − 3 1 = 𝑥→0 𝑥 6 lim

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