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NARA [144]
2 years ago
7

Find the missing segment in the image below.

Mathematics
1 answer:
rjkz [21]2 years ago
6 0
I think the answer might be 3
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Lim (sin x )^tanx as x->pi/2
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 <span>lim (x → π/2) (sinx)^(tanx) 
= lim (x → π/2) e^[(tanx) ln (sinx)] 
= e^ [lim (x → π/2) (tanx) ln (sinx)] ... (1) 

lim (x → π/2) (tanx) ln (sinx) 
= lim (x → π/2) [ln(sinx) / cotx] 

Using L'Hospital'stheorem, 
= lim (x → π/2) [- cotx / cosec^2 x] 
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Plugging in ( 1 ), 
required limit = e^0 = 1 

=>Answer is 1.

I hope my answer has come to your help. Thank you for posting your question here in Brainly.
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