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lim {(integration of F(t) dt) 4m 2 to sec^2 x} divided by {x^2- pi^2/16} x->pi/4

 

lim {(integration of F(t) dt) 4m 2 to sec^2 x} divided by {x^2- pi^2/16}

 

 x->pi/4

Grade:12th pass

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 years ago
Hello Student,
L = \lim_{x\rightarrow \frac{\pi }{4}}\frac{\int_{2}^{sec^{2}x}F(x)dx}{x^{2}-\frac{\pi ^{2}}{16}}
It is zero by zero form. So apply L’hospital rule.
L = \lim_{x\rightarrow \frac{\pi }{4}}\frac{F(sec^{2}x)-F(2)}{2x} = \frac{F(2)-F(2)}{2.\frac{\pi }{4}}
L = 0
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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