KLista 4 k
1. Calcule lim
x→+∞f(x), sabendo que, para
todo x>1, 10ex−21
2ex
<f(x)<5px
px−1.
2. Avalie os limites a seguir indicando todas
as propriedades utilizadas:
(a) lim
x→−∞
3x3−x+1
x2
(b) lim
x→+∞
x6+2x4−3x−8
−2x4+x+1
(c) lim
x→+∞
x3−x2+1
x−1
(d) lim
x→−∞−x5+x3
(e) lim
x→+∞xx2+1
(f) lim
x→+∞px2+1−x
(g) lim
x→+∞
px2+2
2x+1
(h) lim
x→−∞
px2+2
2x+1
(i) lim
x→−∞p4x2+x−2x
(j) lim
x→+∞3
px3+1−x
(k) lim
x→−∞3
px3+x−3
px3+1
(l) lim
x→+∞
qx+px+px
px+1
(m) lim
x→+∞
px+x2
2x−x2
(n) lim
x→+∞
sen(x)
x
(o) lim
x→−∞2xsen3
x
(p) lim
x→+∞
x−cos(x)
x
(q) lim
x→−∞ x2sen(x)
(r) lim
x→+∞
sen2(x)
x2+1
(s) lim
x→+∞
x2
px2+2
(t) lim
x→+∞arctg(2x)
(u) lim
x→+∞
1
4−2x
(v) lim
x→−∞
1
4−2x
(w) lim
x→−∞ln(|x|)
3. Determine aebnúmeros reais tais que
lim
x→+∞px2−x−1−a x −b=0.
4. Avalie o limite
lim
x→+∞px2−2x−1−px2−7x+3.
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