# MATH125 Worksheet 1 - The Area Problem - Math 125, section F, Fall 2020 _ WebAssign.pdf

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Area FunctionsPart 1 of 4 Define A(x) to be the areabounded by the x-axis and the function f(x)=3 between the y-axis and thevertical line at x(see the diagram). Compute the following values: A(2) = 6 A(3) = 9 A(4) = 12 and as a function of xin general, A(x) =\$\$3x(a formula)Graphically, what does A(3)−A(1) correspond to? A(1) = 3 3Here we will examine the area under three basic straight line functions.6912 =31.[27/27 Points]DETAILSPREVIOUS ANSWERSMY NOTES
Part 2 of 4 Compute the following values (give your answers in exact form): Define B(x) to be the areabounded by the x-axis and the function g(x)=1+xbetween the y-axis andthe vertical line at x(see the diagram). B(1) = 3/2 3/2B(2) = 4 B(3) = 15/2 15/2B(4) = 12 and as a function of xin general, B(x) =\$\$x+x22(a formula)Graphically, what does B(3)−B(1) correspond to? Hint Video (.mp4) (Hint: think triangle + rectangle) Hint Video (.mp4) Hint Video (.wmv)412
Part 3 of 4 Compute the following values (give your answers in exact form): Hint Video (.wmv) Define C(x) to be the areabounded by the x-axis and the function h(x)=6−xbetween the y-axis andthe vertical line at x(see the diagram). 1016 (a formula) Graphically, what does C(3)−C(1) correspond to? The area of the trapezoid between \[x=1\] and \[x=3\] with left height 5 and right height 3Hint Video ( mp4)The area of the trapezoid between x=1 and x=3 with left height 5 and right height 3
Part 4 of 4 For each of the above, the areaincreases as xincreases. So A(x), B(x) and C(x) are increasingfunctions even though [f(x)\] is constant, g(x) is increasing and h(x) is decreasing. (There is a difficultywith C(x) when xgets larger than 6, but we'll deal with that later). Solution or ExplanationHint Video (.mp4) Hint Video (.wmv)
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