why is xSin(1/x) same thing as sin(1/x) / (1/x) ?
2007-12-13 04:43:51 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Because if you re-write the sin(1/x) / (1/x) you take the reciprocal of the divisor (1/x) which makes it (x/1) and that equals (x). Thus turning the problem into sin(1/x) times (x/1). Hope that helps.
2007-12-13 04:47:50 · answer #1 · answered by Jeremy K 3 · 0⤊ 0⤋
Because sin(1/x) / (1/x) is a complex fraction (you have a fraction in the denominator.)
Dividing by a fraction is equal to multiplying by the reciprocal of the fraction [1/(1/2) = 1*(2/1) = 2]
The trig function has nothing to do with the problem, as it doesn't change on either side of the equation. You could call it W or whatever, but it it is the same on both sides.
2007-12-13 12:53:33 · answer #2 · answered by Anonymous · 0⤊ 0⤋
xSin(1/x) = sin(1/x) / (1/x) because dividing sin(1/x) by (1/x) is equivalent to multiplying Sin(1/x) by x
2007-12-13 12:54:13 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Because when you divide by a fraction (1/x) you invert the fraction and multiply... so 1/x becomes x/1 or just x.
2007-12-13 12:49:22 · answer #4 · answered by Greg & Jan M 2 · 0⤊ 0⤋
Multiplying by x is the same as dividing by 1/x.
(Of course, x is not 0 here)
2007-12-13 12:49:36 · answer #5 · answered by steiner1745 7 · 0⤊ 0⤋
1. if Sin(1/x)=a then xSin(1/x)=xa
2. if Sin(1/x)=a then Sin(1/x)/(1/x)=a/(1/x)
3. a/(1/x)=(a/1)/(1/x)=ax
4. ax=xa
2007-12-13 12:56:19 · answer #6 · answered by Nikola S 1 · 0⤊ 0⤋