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Question Number 69667 by ahmadshahhimat775@gmail.com last updated on 26/Sep/19

Answered by Kunal12588 last updated on 26/Sep/19

lim_(x→(π/3)) ((sec x −2)/((π/3)−x))  =lim_(x→(π/3)) ((sec x tan x)/(−1))  =−2×(√3)=−2(√3)

$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{3}}} {{lim}}\frac{{sec}\:{x}\:−\mathrm{2}}{\frac{\pi}{\mathrm{3}}−{x}} \\ $$$$=\underset{{x}\rightarrow\frac{\pi}{\mathrm{3}}} {{lim}}\frac{{sec}\:{x}\:{tan}\:{x}}{−\mathrm{1}} \\ $$$$=−\mathrm{2}×\sqrt{\mathrm{3}}=−\mathrm{2}\sqrt{\mathrm{3}} \\ $$

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