What is limx→2x5−32x−2 ?
Answers
Evaluate the limit of the numerator and the limit of the denominator.
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0
0
Since
0
0
is of indeterminate form, apply L'Hospital's Rule. L'Hospital's Rule states that the limit of a quotient of functions is equal to the limit of the quotient of their derivatives.
lim
x
→
2
x
5
−
32
x
−
2
=
lim
x
→
2
d
d
x
[
x
5
−
32
]
d
d
x
[
x
−
2
]
Find the derivative of the numerator and denominator.
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lim
x
→
2
5
x
4
1
Take the limit of each term.
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5
(
lim
x
→
2
x
)
4
lim
x
→
2
1
Evaluate the limits by plugging in
2
for all occurrences of
x
.
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5
(
2
)
4
1
Simplify the answer.
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Divide
5
(
2
)
4
by
1
.
5
(
2
)
4
Remove parentheses.
5
⋅
2
4
Raise
2
to the power of
4
.
5
⋅
16
Multiply
5
by
16
.
80
()|