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Yeah. The figure shows a circular arc of like
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us and a quarter lengths. You want to find
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the limit as data approaches zero from the right of
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us divided by D. So this question is challenging
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the understanding of limits in particular system. An understanding
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of how to construct functions using things in the circles
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and then how to have a limit from there.
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So what this means is first we need to buy
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DNS has function the data if you want to be
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able to value the women above. So we can
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think of D. Using the data including so each
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of the two black legs in the figure. Either
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the or here are the radius of the circle are
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thus for data over to where this angle is bisected
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by the lines in particular, candy, we have
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that over to our side data over two. That's
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the equal to our idea that we know that this
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line bisects the angle and E. Over G.
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Giving us the original on either side simply because these
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two sides are equivalent length. Therefore these angles are
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equivalent. Therefore, we know the line connecting these
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5 60 simply because of geometry principles with here.
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So now that we understand why how we constructed G
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equal to our side data over to we notice I
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think that some of the circumference of the circle is
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two pi R. As is simply the fractional,
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you know, over two pi times the circumference.
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Thus, C gives us equal our data. So
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from here we can put us over D. As
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data divided by two side data over to where the
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Rh equation cancel out one right? That's over D
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. That we have a clear given the black on
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the right. We see that getting towards the right
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hand limit data approaching zero for the right but the
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function approaches value want thus, from the graph,
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which is the limit, as data approaches zero for
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the right after everybody is equal to what we want
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. So