# How do you find the limit of #(sin4x)/(sin6x)# as #x->0#?

As you might have noticed, now we have in the first two terms the known limit

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

To find the limit of (sin4x)/(sin6x) as x approaches 0, we can use the concept of limits and trigonometric identities. By applying the limit properties and the fact that sin(x)/x approaches 1 as x approaches 0, we can simplify the expression.

Using the trigonometric identity sin(2θ) = 2sin(θ)cos(θ), we can rewrite the expression as (2sin(2x)cos(2x))/(2sin(3x)cos(3x)).

Next, we can cancel out the common factors of 2 and sin(2x) to get cos(2x)/(sin(3x)cos(3x)).

Further simplifying, we can rewrite cos(2x) as 1 - 2sin^2(x) and cos(3x) as 1 - 3sin^2(x).

Substituting these values, we get (1 - 2sin^2(x))/(sin(3x)(1 - 3sin^2(x))).

Now, as x approaches 0, sin(x) also approaches 0. Therefore, we can substitute sin(x) with 0 in the expression.

Doing so, we get (1 - 2(0))/(0(1 - 3(0))).

Simplifying further, we have 1/0.

Since division by zero is undefined, the limit of (sin4x)/(sin6x) as x approaches 0 does not exist.

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 is the limit of #(x^2 - 7x)/(x+1)# as x goes to infinity?
- How do you determine the limit of #(2x^2-4x) / (x+1)# as x approaches positive infinity?
- How do you find the limit of #(x^2 - 1) # as x approaches #-2#?
- How do you find the limit of #x^4# as #x->2#?
- How do you find the limit of #(x+5)/(x-5)# as x approaches 5 from the right?

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