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anonymous
 5 years ago
a region in the plane is bounded by the graph of y=1/x, the xaxis, the line x=m and the line x=3m, m>0. the area of this region: a) is independent of m b) increases as m increases c) decreases as m increases d) decreases for all m<1/3 e) increases for all m<1/3
anonymous
 5 years ago
a region in the plane is bounded by the graph of y=1/x, the xaxis, the line x=m and the line x=3m, m>0. the area of this region: a) is independent of m b) increases as m increases c) decreases as m increases d) decreases for all m<1/3 e) increases for all m<1/3

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watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1Interesting question! hold on .... :)

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1The are of the region is given by \[A(m)=\int_m^{3m}\frac{1}{x}\;dx=\int_0^{3m}(1/x)dx\int_0^m (1/x)dx\] By the fundamental theorem of calculus \[A'(m)=\frac{1}{3m}\cdot 3\frac{1}{m}=0\] So the area doesn't change with respect to m. a) is the answer.
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