# How do you find the limit of #(sqrt(x^2+1))/(3x-1)# as x approaches infinity?

The answer are:

This is because:

So:

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

Now taking the limit as x approaches infinity we have

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

To find the limit of (sqrt(x^2+1))/(3x-1) as x approaches infinity, we can use the concept of limits. By dividing both the numerator and denominator by x, we can simplify the expression to (sqrt(1+(1/x^2)))/(3-(1/x)). As x approaches infinity, 1/x approaches 0. Therefore, the expression simplifies to sqrt(1+0)/3, which is equal to 1/3. Hence, the limit of (sqrt(x^2+1))/(3x-1) as x approaches infinity is 1/3.

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 determine the limit of #(x+2)/(3x^2)# as x approaches 0-?
- How do you find #lim root3(t^3+1)-t# as #t->oo#?
- What is the limit of #(1 + 2/x)^x# as x approaches infinity?
- What are the removable and non-removable discontinuities, if any, of #f(x)=(x - 2) / (x^2 - 3x + 2 )#?
- What is the limit of # (x-x^(1/2))# as x goes to infinity?

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