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when the curves y= log x(base 10) and y= 1/x are drawn in the x-y plane, how many times do they intersect for values x>=1 ?

2006-10-20 01:28:03 · 1 answers · asked by Anonymous in Science & Mathematics Mathematics

1 answers

Once.

log(x) has an asymptote of x=0 and increases as x get's larger. It crosses the x-axis at the point (1,0) and then slowly reaches to infinity.

1/x only appears in the first and third quadrant of the cartesian plane. It's asymptotes are the x and y-axis, and so it never crosses them.

The only place where 1/x and log(x) would meet is in the first quadrant (where x and y are both positive), and since log(x) slowly goes towards infinity as 1/x approaches zero in the same direction they can only cross once (because neither of them changes direction.)

2006-10-20 01:54:01 · answer #1 · answered by Leah H 2 · 0 0

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