求高数大神解答
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(1)
lim(x->0) (1+sinx)^cscx
=lim(x->0) (1+sinx)^(1/sinx)
=lim(x->0) (1+x)^(1/x)
=e
(2)
let
y= π/2 -x
lim(x->π/2) (1 + cosx)^(secx)
=lim(x->π/2) (1 + cosx)^(1/cosx)
=lim(y->0) (1 + siny)^(1/siny)
=lim(y->0) (1 + y)^(1/y)
=e
lim(x->0) (1+sinx)^cscx
=lim(x->0) (1+sinx)^(1/sinx)
=lim(x->0) (1+x)^(1/x)
=e
(2)
let
y= π/2 -x
lim(x->π/2) (1 + cosx)^(secx)
=lim(x->π/2) (1 + cosx)^(1/cosx)
=lim(y->0) (1 + siny)^(1/siny)
=lim(y->0) (1 + y)^(1/y)
=e
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