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lim-x-0-tan-x-2-sin-x-2-x-2-x-2-x-2-x-2-2x-2-




Question Number 199553 by cortano12 last updated on 05/Nov/23
  lim_(x→0)  ((tan ((x/2))−sin ((x/2)))/(x^2  ((√(x^2 +x−2))−(√(x^2 +2x−2)) ))) =?
$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)−\mathrm{sin}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)}{\mathrm{x}^{\mathrm{2}} \:\left(\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}−\mathrm{2}}−\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}−\mathrm{2}}\:\right)}\:=? \\ $$
Answered by MM42 last updated on 05/Nov/23
−((√2)/8) i  ✓
$$−\frac{\sqrt{\mathrm{2}}}{\mathrm{8}}\:{i}\:\:\checkmark \\ $$

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