# How do you use the Squeeze Theorem to find #lim x^2 (Sin 1/x)^2 # as x approaches zero?

We are aware of that

Since

As per the squeeze theorem,

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

To use the Squeeze Theorem to find the limit of the function lim x^2 (Sin 1/x)^2 as x approaches zero, we need to find two other functions that "squeeze" the given function and have the same limit as x approaches zero.

First, we can observe that -1 ≤ Sin(1/x) ≤ 1 for all x ≠ 0. Therefore, we can square this inequality to get 0 ≤ (Sin(1/x))^2 ≤ 1.

Next, we multiply the inequality by x^2 to get 0 ≤ x^2(Sin(1/x))^2 ≤ x^2.

Since the limit of x^2 as x approaches zero is also zero, we can conclude that the limit of x^2(Sin(1/x))^2 as x approaches zero is also zero, based on the Squeeze Theorem.

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

- How do you prove that the function f(x) = | x | is continuous at x=0, but not differentiable at x=0?
- How do you evaluate #(x−4 )/ (x^2+6x−40)# as x approaches 4?
- How do you use a graphing calculator to find the limit of #(12(sqrtx-3))/(x-9)# as x approaches 0?
- How do you know a limit does not exist?
- What is the limit of #(4x)/(x-6)+(5x)/(x+6)# as x approaches infinity?

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