# What is the farthest apart the particles ever get if the positions of two particles on the s-axis are #s_1=cos(t)# and #s_2=cos(t+pi/4)#?

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The farthest apart the particles ever get is when their positions are maximally distant from each other. To find this, we calculate the maximum separation between the positions s₁ = cos(t) and s₂ = cos(t + π/4) by finding the maximum difference between the values of these functions. This occurs when the difference between cos(t) and cos(t + π/4) is maximized. By using trigonometric identities, we can simplify this to find the maximum distance between the two positions.

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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.

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