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Unformatted text preview: g ; give its domain in interval notation. Write a simpliﬁed formula for the function k = ( f + g ) ◦ h ; give its domain in interval notation. k ( x ) = 1-x + √ x ; Domain: [ 0 , 1 ] 4. A rectangle is fashioned so that its area and perimeter have the same numeric value. Write the length ‘ of the rectangle as a function of the width w . What is the only square that behaves this way? 5. A company manufactures a gutter by bending up the sides of a metal sheet of ﬁxed width w = 2 ft, so that cross-sections form an isosceles trapezoid with desired length b = 1 ft for the smaller base as shown. Express the cross-sectional area as a function of the angle θ . For fun, experiment with a calculator to try to decide what θ maximizes the cross-sectional area. note that the triangle shown has sides 1 2 sin( θ ) and 1 2 cos( θ )...
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- Spring '08