How do you find the Limit of #n^( ln( (n+1)/n )# as n approaches infinity?
1
By signing up, you agree to our Terms of Service and Privacy Policy
To find the limit of n^(ln((n+1)/n)) as n approaches infinity, we can use the properties of logarithms and exponential functions.
First, we can simplify the expression inside the logarithm by dividing (n+1) by n:
ln((n+1)/n) = ln(n+1) - ln(n)
Next, we substitute this simplified expression back into the original equation:
n^(ln((n+1)/n)) = n^(ln(n+1) - ln(n))
Using the property of logarithms, we can rewrite this as:
n^(ln(n+1) - ln(n)) = n^(ln(n+1)) / n^(ln(n))
Now, let's consider the behavior of each term as n approaches infinity:
As n approaches infinity, ln(n+1) and ln(n) both approach infinity, but ln(n+1) grows slightly faster.
Similarly, as n approaches infinity, n^(ln(n+1)) and n^(ln(n)) both approach infinity, but n^(ln(n+1)) grows significantly faster.
Therefore, the limit of n^(ln((n+1)/n)) as n approaches infinity is infinity.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- How do you find the limit of #x/sqrt(9-x^2)# as x approaches -3+?
- How do you find the limit of #sqrt(x^2-9)/(2x-6)# as x approaches #-oo#?
- How do you find the Limit of #2x+5# as #x->-3# and then use the epsilon delta definition to prove that the limit is L?
- Find limits as x approaches positive and negative infinity of function f(x)= 4x^3 -x^4 ?
- How do you find any asymptotes of #f(x)=(x+3)/(x^2-4)#?
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7