How do you evaluate the limit #sin^3(2x)/sin^2(3x)# as x approaches #0#?
After the textbook result
then
By signing up, you agree to our Terms of Service and Privacy Policy
To evaluate the limit of sin^3(2x)/sin^2(3x) as x approaches 0, we can use the properties of limits and trigonometric identities. By applying the limit properties, we can simplify the expression:
lim(x→0) sin^3(2x)/sin^2(3x) = (lim(x→0) sin(2x))^3 / (lim(x→0) sin(3x))^2
Using the trigonometric identity lim(x→0) sin(x)/x = 1, we can rewrite the expression further:
= (2/2)^3 / (3/3)^2 = 1/1 = 1
Therefore, the limit of sin^3(2x)/sin^2(3x) as x approaches 0 is equal to 1.
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.
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 #lim_(xrarr0+)(ln x) / (csc x)#?
- How do you determine the limit of #e^x/(x-5)^3# as x approaches 5-?
- How do you use the definition of continuity and the properties of limits to show that the function #g(x) = sqrt(-x^2 + 8*x - 15)# is continuous on the interval [3,5]?
- How do you use the Squeeze Theorem to find #lim (x^2)(cos20(pi*x)) # as x approaches zero?
- What are the removable and non-removable discontinuities, if any, of #f(x)=(x^4 - 1)/(x-1) #?

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