find limit 2^((x-1)/x) as x approaches infinty?
please help me find limit of 2^((x-1)/x) as x approaches infinty, it must be equal 1 but im always getting 2 as a result. Thanks in advance.
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please help me find limit of 2^((x-1)/x) as x approaches infinty, it must be equal 1 but im always getting 2 as a result. Thanks in advance.
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y = lim(x > inf) 2^((x-1)/x)
take the natural log of each side
lny = lim(x > inf) ((x - 1) / x) ln2
= ln2 lim(x > inf) (x - 1) / x
multiply the fraction by 1/x / 1/x
= ln2 lim(x > inf) 1 - 1 / x
1 / x goes to zero as x goes to infinity
= ln2
lny = ln2
e^lny = e^ln2
y = 2
I got 2 too, so maybe it is the right answer?
2^((x-1)/x) as x approaches infinty?
Ans
2