find the limit. (if the limit is infinite, enter ∞ or -∞, as appropriate. if the\n\nlim\nx→(π/2)^…

find the limit. (if the limit is infinite, enter ∞ or -∞, as appropriate. if the\n\nlim\nx→(π/2)^- e^{sec(x)}\n\nresources\nread it

find the limit. (if the limit is infinite, enter ∞ or -∞, as appropriate. if the\n\nlim\nx→(π/2)^- e^{sec(x)}\n\nresources\nread it

Answer

Explanation:

Step1: Analyze the behavior of (\sec(x))

As (x\to(\frac{\pi}{2})^{-}), (\cos(x)\to0^{+}). Since (\sec(x)=\frac{1}{\cos(x)}), then (\sec(x)\to+\infty) as (x\to(\frac{\pi}{2})^{-}).

Step2: Analyze the behavior of the exponential function

We know that the function (y = e^{u}) is a continuous function. When (u=\sec(x)) and (u\to+\infty), by the property of the exponential function (y = e^{u}) (where (\lim_{u\to+\infty}e^{u}=+\infty)).

Answer:

(\infty)