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

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

choose me best thanks

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