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Tardigrade
Question
Mathematics
Let f(x)=(1/3) x sin x-(1- cos x). The smallest positive interger k such that lim limits x arrow 0 (f(x)/x) ≠ 0
Q. Let
f
(
x
)
=
3
1
x
sin
x
−
(
1
−
cos
x
)
. The smallest positive interger
k
such that
x
→
0
lim
x
f
(
x
)
=
0
2278
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A
4
B
3
C
2
D
1
Solution:
lim
x
→
0
x
k
f
(
x
)
=
lim
x
→
0
x
k
3
x
s
i
n
x
−
1
+
c
o
s
x
[
0
0
form
]
=
lim
x
→
0
k
x
k
−
1
3
s
i
n
x
+
3
x
c
o
s
x
−
s
i
n
x
[
0
0
form
]
=
lim
x
→
0
k
(
k
−
1
)
x
k
−
2
3
c
o
s
x
+
3
c
o
s
x
−
3
x
s
i
n
x
−
c
o
s
x
=
0
if
k
=
2