Find the smallest number x such that tan e ^x is undefined.

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Find the smallest number x such that tan e ^x is undefined.

Round your answer to five decimal places.
Sep 24th, 2014

e^x = pi 
turns into.. 
ln pi = x 

tan(t) = sin(t) / cos(t) 

tan(t) is undefined where cos(t) = 0 
tan(t) is zero where sin(t) = 0 

cos(t) = 0 at t = pi/2 + n pi; n integer 
sin(t) = 0 at t = n pi; n integer 

e^x = exp(x) >= 0 for all x 
so t < 0 aren't included. 

So the smallest t are those closest to, but not equal to zero. 
For sin(t) = 0, t = pi 
For cos(t) = 0, t = pi/2 

tan(exp(x)) = 0 when x = ln(pi) 
tan(exp(x)) undefined when x = ln(pi/2)

choose me best thanks

Sep 24th, 2014

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