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44 Elementos de cálculo, volumen 1<br />
Ejemplo 9.<br />
a) lim<br />
x→3 (x + 15) = lim<br />
x→3 x + lim<br />
x→3 15 = 3 + 15 = 18<br />
b) lim<br />
x→3 (x − 15) = lim<br />
x→3 x − lim<br />
x→3 15 = 3 − 15 = −12<br />
c) lim<br />
x→5 4x = lim<br />
x→5 4 · lim<br />
x→5 x = 4 · 5 = 20<br />
x + 15<br />
d) lim<br />
x→3<br />
e) lim<br />
x→2 x 3 =<br />
x − 15 = limx→3(x + 15)<br />
limx→3(x − 15)<br />
<br />
lim<br />
x→2 x<br />
3<br />
= 2 3 = 8<br />
18 −3<br />
= =<br />
−12 2<br />
√ <br />
f) lim x = lim x =<br />
x→4<br />
x→4 √ 4 = 2<br />
. △<br />
Ejemplo 10.<br />
Calcular lim<br />
x→2 (x 2 + 2x + 3).<br />
Solución: Tenemos<br />
lim<br />
x→2 (x2 + 2x + 3) = lim x<br />
x→2 2 + lim 2x + lim 3<br />
x→2 x→2<br />
<br />
= lim<br />
x→2 x<br />
2 + lim 2 · lim x + lim 3<br />
x→2 x→2 x→2<br />
= 2 2 + 2 · 2 + 3<br />
= 4 + 4 + 3<br />
= 11<br />
. △<br />
Ejemplo 11.<br />
x<br />
lim<br />
x→3<br />
2 + 1<br />
x + 2 = [limx→3 x] 2 + limx→3 1<br />
limx→3 x + limx→3 2<br />
= 32 + 1<br />
3 + 2<br />
= 10<br />
.<br />
= 2<br />
5<br />
△
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