# How do you find the limit of #xtan(1/(x-1))# as x approaches infinity?

The limit is 1. Hopefully someone on here can fill in the blanks in my answer.

Multiplying by the x gives:

So, because all the terms apart from the first have an x on the denominator and constant on the numerator

because all terms after the first will tend to zero.

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

To find the limit of xtan(1/(x-1)) as x approaches infinity, we can use the fact that the limit of tan(x) as x approaches infinity is undefined. Therefore, we need to simplify the expression.

By applying the limit properties, we can rewrite the expression as (1/(x-1))/cot(1/(x-1)). As x approaches infinity, 1/(x-1) approaches 0. Using the limit properties again, we can rewrite the expression as 1/cot(0).

The cotangent function is the reciprocal of the tangent function, so cot(0) is equal to 1/tan(0). The tangent function is undefined at 0, so 1/tan(0) is also undefined.

Therefore, the limit of xtan(1/(x-1)) as x approaches infinity is undefined.

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.

- What kind of functions have horizontal asymptotes?
- What is the limit of #(1+4/x)^x# as x approaches infinity?
- How do you find the limit of #(e^x - 1)/x^3# as x approaches 0?
- How do you evaluate the limit #1/(x-1)+e^(x^2)# as x approaches #1^-#?
- How do you determine the limit of #cot(x)# as x approaches #pi^-#?

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