# How do you use the Squeeze Theorem to find #lim xcos(50pi/x)# as x approaches zero?

See the explanation.

So,

Dual-sided Limit

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To use the Squeeze Theorem to find lim xcos(50pi/x) as x approaches zero, we can start by noting that -1 ≤ cos(50pi/x) ≤ 1 for all x ≠ 0.

Next, we can multiply each part of the inequality by x to get -x ≤ xcos(50pi/x) ≤ x for all x ≠ 0.

Since the limit of -x as x approaches zero is 0, and the limit of x as x approaches zero is also 0, we can conclude that the limit of xcos(50pi/x) as x approaches zero is also 0.

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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 #(x+sinx)/x# as x approaches 0?
- How do you find #lim_(x to 0) xcos(1/x)#?
- What is the limit as x approaches infinity of a constant?
- How do you find the limit of #x*sin(1/x)# as x tends to positive infinity?
- How do you find the limit of #((x^2)-x-2)/(x-1)# as x approaches #1^+#?

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