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Problem
Problem
For
a
>
0
a > 0
a
>
0
, let
l
=
lim
x
→
π
2
−
a
cot
x
−
a
cos
x
cot
x
−
cos
x
l = \lim_{x \to \frac{\pi}{2}^-} \frac{a^{\cot x} - a^{\cos x}}{\cot x - \cos x}
l
=
lim
x
→
2
π
−
c
o
t
x
−
c
o
s
x
a
c
o
t
x
−
a
c
o
s
x
and
m
=
lim
x
→
∞
(
x
2
+
a
x
−
x
2
−
a
x
)
m = \lim_{x \to \infty} (\sqrt{x^2 + ax} - \sqrt{x^2 - ax})
m
=
lim
x
→
∞
(
x
2
+
a
x
−
x
2
−
a
x
)
, then a.
l
>
m
l > m
l
>
m
, for all
a
>
0
a > 0
a
>
0
b.
l
>
m
l > m
l
>
m
, only when
a
≥
1
a \ge 1
a
≥
1
c.
l
>
m
l > m
l
>
m
, for all
a
>
e
−
a
a > e^{-a}
a
>
e
−
a
d.
e
l
+
m
=
0
e^l + m = 0
e
l
+
m
=
0
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