# How do you compute the limit of #cot(4x)/csc(3x)# as #x->0#?

The limit of a product/quotient is the product/quotient of the limits:

Now:

And:

So we have:

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

To compute the limit of cot(4x)/csc(3x) as x approaches 0, we can simplify the expression using trigonometric identities.

Recall that cot(x) is equal to 1/tan(x), and csc(x) is equal to 1/sin(x).

Using these identities, we can rewrite the expression as (1/tan(4x))/(1/sin(3x)).

Next, we can simplify further by multiplying the numerator and denominator by sin(4x)/sin(4x), which gives us sin(3x)/(tan(4x)*sin(4x)).

Now, we can use the fact that sin(x)/x approaches 1 as x approaches 0, and tan(x)/x also approaches 1 as x approaches 0.

Therefore, the limit of cot(4x)/csc(3x) as x approaches 0 is equal to sin(3x)/(tan(4x)*sin(4x)), which simplifies to 3/4.

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 find the limit #(x^-1+x^(-1/2))/(x+x^(-1/2))# as #x->1^+#?
- How do you find the limit of #((5x^2-2)^(1/2))/(x+3)# as x approaches #-oo#?
- How do you find the limit of # abs(x-2) / (x-2)# as x approaches #2^+#?
- How do you find #lim sqrt(x^2+1)-x# as #x->oo#?
- How do you evaluate the limit #2# as x approaches #0#?

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