As approaches from the left

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

As xx approaches π2\dfrac{\pi}{2} from the left, what is the limiting behavior of ddx(tan⁡x)\dfrac{d}{dx}(\tan x)? State whether the derivative tends to +∞+\infty, −∞-\infty, or a finite value, and indicate the sign.

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