Solve the given rational equation for ( x ) over the interval ( [0, 2pi] ): ( frac{1}{x} = sin(x) )

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Accepted Answer

Step:1 ：First, get rid of the fraction by multiplying both sides of the equation by (x): ( 1 = x sin(x) )Step:2 ：Then, to isolate (x), set the equation equal to zero: (x sin(x) - 1 = 0)Step:3 ：This equation cannot be solved algebraically. So we use a graphing calculator or software to find the intersections of (y = x sin(x)) and (y = 1) over the interval ( [0, 2pi] )Step:4 ：From the graph, we find that the two curves intersect at approximately ( x = 1.114 ) and ( x = 2.03 ) within the given interval

Answer

Step: 1 ：First, get rid of the fraction by multiplying both sides of the equation by (x): ( 1 = x sin(x) )Step: 2 ：Then, to isolate (x), set the equation equal to zero: (x sin(x) - 1 = 0)Step: 3 ：This equation cannot be solved algebraically. So we use a graphing calculator or software to find the intersections of (y = x sin(x)) and (y = 1) over the interval ( [0, 2pi] )Step: 4 ：From the graph, we find that the two curves intersect at approximately ( x = 1.114 ) and ( x = 2.03 ) within the given interval

Solve the given rational equation for $x$ over the interval $[0, 2 π]$ : $\frac{1}{x} = \sin (x)$

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Solve the given rational equation for $x$ over the interval $[0, 2 π]$ : $\frac{1}{x} = \sin (x)$