` Evaluate `:lim_(x rarr0)(e^(2x)-1)/(x)
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Popular Problems Calculus Evaluate ( limit as x approaches 0 of e^(2x)-1)/x
lim
x
→
0
e
2
x
−
1
x
Take the limit of each term.
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Apply L'Hospital's rule.
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lim
x
→
0
2
e
2
x
Move the term
2
outside of the limit because it is constant with respect to
x
.
2
lim
x
→
0
e
2
x
Move the limit into the exponent.
2
e
lim
x
→
0
2
x
Move the term
2
outside of the limit because it is constant with respect to
x
.
2
e
2
lim
x
→
0
x
Evaluate the limit of
x
by plugging in
0
for
x
.
2
e
2
⋅
0
Multiply
2
by
0
.
2
e
0
Anything raised to
0
is
1
.
2
⋅
1
Multiply
2
by
1
.
2
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