大学文科数学求极限
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(7)
y=1/x
lim(x->∞) x^2. [sin(1/x)]^2
=lim(y->0) (siny)^2/y^2
=lim(y->0) y^2/y^2
=1
(9)
y=3x
lim(x->0) (1+3x)^(1/x)
=lim(y->0) (1+y)^(3/y)
=e^3
(11)
lim(x->0) sin(x^2)/(sinx)^3
=lim(x->0) (x^2)/(x)^3
=lim(x->0) 1/x
->∞
y=1/x
lim(x->∞) x^2. [sin(1/x)]^2
=lim(y->0) (siny)^2/y^2
=lim(y->0) y^2/y^2
=1
(9)
y=3x
lim(x->0) (1+3x)^(1/x)
=lim(y->0) (1+y)^(3/y)
=e^3
(11)
lim(x->0) sin(x^2)/(sinx)^3
=lim(x->0) (x^2)/(x)^3
=lim(x->0) 1/x
->∞
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