lim x_0( sinx)^ tanx
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Answered by
1
Answer:
Step-by-step explanation:Answer:
−
∞
Explanation:
Recall
sin
(
−
x
)
=
−
sin
(
x
)
Therefore we have
lim
x
→
0
−
sin
x
tan
x
−
x
Substitution yields
−
sin
0
tan
0
−
0
which simplifies to
−
0
0
This is indeed indeterminate so we can use L'Hopital's Rule which states
lim
x
→
0
−
sin
x
tan
x
−
x
=
lim
x
→
0
d
d
x
(
−
sin
x
)
d
d
x
(
tan
x
−
x
)
This result in
lim
x
→
0
−
cos
x
sec
2
x
−
1
Substitution gives
−
cos
0
sec
2
(
0
)
−
1
This results in
−
1
1
−
1
→
−
1
0
this tends toward
−
∞
∴
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