Evaluate-lim-x-pi-2-tan2x-x-pi-2-

Question Number 25068 by NECx last updated on 02/Dec/17

E v a l u a t e

\lim_{x \to \frac{π}{2}} (\frac{t a n 2 x}{x - π / 2})

Answered by jota+ last updated on 03/Dec/17

U s e H o p i t a l r u l e

= \frac{\lim_{x \to π / 2} {(t a n 2 x)}^{'}}{\lim_{x \to π / 2} {(x - π / 2)}^{^{'}}} = \frac{\lim_{x \to π / 2} 2 / {c o s}^{2} 2 x}{\underset{x \to π / 2}{\lim 1}} = 2

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