- Calcule, se existirem, os seguintes limites:
a) lim (x→1) (x²−1)/(x²−1)
b) lim (x→2) (x³−8)/(x−2)
c) lim (x→0) x/(x+3)
d) lim (x→0) (x³+7x)/x
e) lim (x→1) (x²−x)/(x²+2x−3)
f) lim (x→2) (x²−5x+6)/(x²−12x+20)
g) lim (x→0) ((4+x)²−16)/x
h) lim (x→3) (x³−27)/(x²−5x+6)
i) lim (x→2) (x²−3x−2)/(3x−6)
j) lim (x→1) √(x²−1)/(x−1)
k) lim (x→0) (x²+9−3)/x²
l) lim (x→4) (x³+5x+4)/(x²+3x−4)
m) lim (x→∞) (x⁴−x²+3x+1)/(7x³−3x⁴)
n) lim (x→∞) (10x²−3x+4)/(3x²−5x+1)
o) lim (x→∞) (x²−3x+1)/(2x²+1)
p) lim (x→∞) (x²+3x+1)/x
q) lim (x→∞) (x²−1)/(x−1)
r) lim (x→∞) (2x⁴+3x²+2x+1)/(4−x²)
s) lim (x→∞) (x²+3x−1)/(x³−2)
t) lim (x→0) sen(9x)/sen(x)
u) lim (x→0) sen(2x)/sen(4x)
v) lim (x→0) (sen²x)/x²
w) lim (x→0) tg(5x)/sen(7x)
x) lim (x→∞) (x/(x+1))^x
y) lim (x→∞) (1+(10/x))^x
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Seja f(x) = 7 + √(x−1). Calcule, caso exista, lim (x→1-) f(x), lim (x→1+) f(x) e lim (x→1) f(x).
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Seja f(x) = { |x|, se x < 4; −4x + 20, se x > 4. Calcule, se existirem, lim (x→4-) f(x), lim (x→4+) f(x) e lim (x→4) f(x).
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Seja f(x) = { x², se x < 1; −1, se x = 1; x + 1, se x > 1. Calcule, se existirem, lim (x→1-) f(x), lim (x→1+) f(x) e lim (x→1) f(x).
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Dada a função f(x) = |x−2|/(x−2), determine lim (x→2-) f(x) e lim (x→2+) f(x).
