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Solve lim(x->pi/3) sin(pi/3-x)/(2cosx – 1)

Solve
lim(x->pi/3) sin(pi/3-x)/(2cosx – 1)

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

L = \lim_{x\rightarrow \frac{\pi }{3}}\frac{sin(x-\frac{\pi }{3})}{2cosx - 1}
It is 0/0 form. Apply L’Hospital
L = \lim_{x\rightarrow \frac{\pi }{3}}\frac{cos(x-\frac{\pi }{3})}{-2sinx}
L = \lim_{x\rightarrow \frac{\pi }{3}}\frac{cos(\frac{\pi }{3}-\frac{\pi }{3})}{-2sin\frac{\pi }{3}}
L = \frac{cos(0)}{-2sin\frac{\pi }{3}}
L = \frac{1}{-2.\frac{\sqrt{3}}{2}}
L = \frac{-1}{\sqrt{3}}

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