anonymous
  • anonymous
a region in the plane is bounded by the graph of y=1/x, the x-axis, 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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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watchmath
  • watchmath
Interesting question! hold on .... :)
watchmath
  • watchmath
The 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.
anonymous
  • anonymous
thanks!:)

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