一道求极限的数学题！求解
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(14)
x->0
sinx ~ x
sin2x ~ 2x
lim(x->0) (1+sinx)^(csc2x)
=lim(x->0) (1+sinx)^[1/(sin2x)]
=lim(x->0) (1+x)^[1/(2x)]
=e^(1/2)
(7)
lim(x->0) sin(3x)/x
=lim(x->0) (3x)/x
=3
(8)
y=x-1
lim(x->1) sin(x^2-1)/(x-1)
=lim(x->1) sin[(x-1)(x+1)]/(x-1)
=lim(y->0) sin[y(y+2)]/y
=lim(y->0) [y(y+2)]/y
=lim(y->0) (y+2)
=2
x->0
sinx ~ x
sin2x ~ 2x
lim(x->0) (1+sinx)^(csc2x)
=lim(x->0) (1+sinx)^[1/(sin2x)]
=lim(x->0) (1+x)^[1/(2x)]
=e^(1/2)
(7)
lim(x->0) sin(3x)/x
=lim(x->0) (3x)/x
=3
(8)
y=x-1
lim(x->1) sin(x^2-1)/(x-1)
=lim(x->1) sin[(x-1)(x+1)]/(x-1)
=lim(y->0) sin[y(y+2)]/y
=lim(y->0) [y(y+2)]/y
=lim(y->0) (y+2)
=2
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