Question 1026315
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let f(x)=sin(x)(e^-x), 0<= x <= 2pi. Find (a) the domain of f and the x- and y- intercepts; (b) the critical numbers and the intervals on which f is increasing or decreasing; (c) the local max and min values; (d) the intervals on which f is concave upward or concave downward; (e) the points of inflection; (f) the graph of f
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The domain of f(x) is the given interval  0<= x <= 2pi.

Zeros of f(x) are the same as zeros sin(x), i.e. 0, pi and 2pi on a given interval.<TABLE>
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{{{graph( 330, 330, -1.5, 7.5, -2.5, 2.5,
          sin(x)*e^(-x)
)}}}


<B>Figure</B>. Plot of  {{{sin(x)*e^(-x)}}}.

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