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

Question

Keegan Hendricks

Mathematics

14 March, 09:54

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

+1

Answers (1)

Know the Answer?

Genevieve Hoover · Answer 1

The correct option is a) : "i s independent of m ".

By the fundamental theorem of calculus: A′ (m) = 1 3m ⋅3 - 1m

=0 So the area doesn't change with respect to m.

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 mb) increases as m increasesc) decreases as m increasesd) decreases for all m<1/3e) increases for all m<1/3

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