# How do you find the limit #(sqrt(y+1)+sqrt(y-1))/y# as #y->oo#?

The limit is

By signing up, you agree to our Terms of Service and Privacy Policy

To find the limit of (sqrt(y+1) + sqrt(y-1))/y as y approaches infinity, we can use the concept of limits.

First, we simplify the expression by multiplying both the numerator and denominator by the conjugate of the numerator, which is (sqrt(y+1) - sqrt(y-1)). This will help us eliminate the square roots in the numerator.

After simplifying, we get (y+1) - (y-1) in the numerator, which simplifies to 2. The denominator remains as y.

Therefore, the limit of (sqrt(y+1) + sqrt(y-1))/y as y approaches infinity is 2.

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.

- How do you evaluate the limit #x-2# as x approaches #1#?
- For what values of x, if any, does #f(x) = secx # have a vertical asymptote?
- What is the limit of #(x^4 + x^5)# as x approaches infinity?
- What are the asymptotes of #f(x)=-x/((x-1)(x^2-4)) #?
- How do you find the limit of #(e^x + x)^(1/X)# as x approaches infinity?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7