Cálculo integral em R
Cálculo integral em R
Cálculo integral em R
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Exercícios<br />
Vejamos um ex<strong>em</strong>plo:<br />
pois lim<br />
x→∞<br />
Calcule os seguintes limites:<br />
x<br />
1. lim<br />
x→4<br />
2 − 16<br />
x − 4 .<br />
2. lim<br />
x→ π<br />
2<br />
−<br />
tg x<br />
sec 2 x .<br />
sin x<br />
3. lim<br />
x→0 cos x − 1 .<br />
√<br />
x<br />
4. lim .<br />
x→+∞ ex 5. lim<br />
x→0 +<br />
√<br />
x log x.<br />
6. lim<br />
x→+∞ x<br />
<br />
π<br />
<br />
− arctgx .<br />
2<br />
7. lim<br />
x→0 + xsinx .<br />
8. lim<br />
x→1 + xlog x .<br />
9. lim<br />
x→ π −<br />
2<br />
10. lim<br />
x→ π<br />
2<br />
−<br />
11. lim<br />
x→+∞<br />
[tg x − sec x].<br />
tg x<br />
sec 2 x .<br />
+∞−∞<br />
lim [log x − x]<br />
x→+∞<br />
x<br />
ex = 0+ e<br />
uma vez que lim<br />
x→∞<br />
x<br />
x<br />
<br />
x 2 − x4 <br />
+ 3x .<br />
1.7. INTEGRAL IMPR ÓPRIO<br />
=<br />
=<br />
lim<br />
x→+∞<br />
<br />
elog x<br />
log<br />
ex <br />
0<br />
0<br />
= lim<br />
x→+∞ log<br />
<br />
x<br />
ex <br />
= −∞,<br />
log elog x−x<br />
= +∞ (cf. ex<strong>em</strong>plo 1(d)).<br />
ISA/UTL – Licões de Mat<strong>em</strong>ática – 2005 55
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