| ucf18-004 A point is moving along the x-axis: At \( t = 0 \) it is at the origin; for \( 0 \leq t<1 \) its velocity is given by \( v(t) = 2t-1 \); for \( 1\leq t<2 \) its velocity is given by \( v(t) = 4t-2 \), for \( 2\leq t\leq 3 \) its velocity is given by \( v(t) = 6t-3 \). Where is the point at \( t=3 \) ? Sketch a rough graph of the point's motion. |
| ucf19-005
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| ucf20-006 Consider the unit circle sketched below. Write as a definite integral (or sum or difference of integrals) the areas of the regions listed to the right of the figure. DO NOT EVALUATE THE INTEGRALS. |
| utf01-008 A cake has dimensions $15'' \times 15'' \times 3''$. It is frosted on the sides and top. How can it be divided into 5 pieces so that each piece has the same amount of cake and the same amount of frosting? What if the dimensions are changed? What about 6 pieces? 7 pieces? $n$ pieces? |
| utf02-005
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