show that Lt limit X tends to zero e to the power 3 + x minus e to the power 3 divided by X is equals to 3
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Explanation:
x→0
lim
sin3
x
8
x
−3
x
As numerator & denominator both tend to zero, we can use L Hospitals rule
x→0
lim
sin3
x
8
x
−3
x
=
x→0
lim
3cos3
x
8
x
log
e
8−3
x
log
e
3
=
3
log
e
3
9
=ln(
3
8
)
1/3
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