# How do you use the Squeeze Theorem to find #lim(x-1)sin(pi/x-1) # as x approaches one?

Since

As per the squeeze theorem,

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

The right-hand limit is 0.

The left limit is 0.

Consequently,

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-1)sin(pi/x-1) as x approaches one, we can start by observing that the sine function is bounded between -1 and 1 for all values of x.

Next, we can rewrite the given function as sin(pi/(x-1)) and notice that as x approaches one, the denominator (x-1) approaches zero.

Using the Squeeze Theorem, we can establish two additional functions that bound the given function. Let's consider the functions f(x) = -1 and g(x) = 1.

Since sin(pi/(x-1)) is bounded between -1 and 1, we have -1 ≤ sin(pi/(x-1)) ≤ 1 for all x ≠ 1.

Therefore, by the Squeeze Theorem, as x approaches one, the limit of sin(pi/(x-1)) is also between -1 and 1.

Hence, the limit of the function lim(x-1)sin(pi/x-1) as x approaches one is 0.

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 of #ln(lnx) / x# as x approaches infinity?
- Suppose #lim_(x→0 +)f(x) = A and lim_(x→0 -)f(x) = B.# Determine #a. lim_(x→0−) f(x^2 − x)# #b. lim_(x→0−)(f(x^2) − f(x))# #c. lim_(x→0+)f(x^3 − x)# #d. lim_(x→0−)(f(x^3) − f(x))# #e. lim_(x→1−)f(x^2 − x)#?
- What is the limit as x approaches infinity of #sin(x)#?
- How do you prove limit of #14-5x=4# as #x->2# using the precise definition of a limit?
- How do you prove the statement lim as x approaches 2 for #(x^2 - 4x + 5) = 1# using the epsilon and delta definition?

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