# For #f(t)= (cos2t,sin^2t)# what is the distance between #f(pi/4)# and #f(pi)#?

Distance between

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To find the distance between two points in the plane, you can use the distance formula:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Given f(t) = (cos^2(t), sin^2(t)), the points f(pi/4) and f(pi) are:

f(pi/4) = (cos^2(pi/4), sin^2(pi/4)) = (1/2, 1/2) f(pi) = (cos^2(pi), sin^2(pi)) = (1, 0)

Using the distance formula:

Distance = sqrt((1 - 1/2)^2 + (0 - 1/2)^2) = sqrt((1/2)^2 + (-1/2)^2) = sqrt(1/4 + 1/4) = sqrt(1/2) = 1/sqrt(2) = sqrt(2)/2

So, the distance between f(pi/4) and f(pi) is sqrt(2)/2.

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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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