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(5)
(i)
|sinx|≤1
lim(x->∞) 1/(3x)=0
=>lim(x->∞) sinx/(3x) =0
(ii)
y=1/x
lim(x->∞) xsin(1/x)
=lim(y->0) siny/y
=1
(iii)
y=x-1
lim(x->1) sin(x-1)/(x-1)
=lim(y->0) siny/y
=1
(iv)
|sin(1/x)|≤1
lim(x->0) x=0
=>lim(x->0) x.sin(1/x) = 0
(6)
(i)
lim(x->0) (1-x)^(1/x) = 1/e
(ii)
lim(x->0) (1+3x)^(1/x) = e^3
(iii)
lim(x->∞) (1+2/x)^x = e^2
(iv)
lim(x->∞) [(x-2)/(x+2)^](x+2)
=lim(x->∞) [1 + 4/(x+2)^](x+2)
=e^4
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