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if limit x tends to a ,find the value of (2-x/a)^tan(πx/2a)

if limit x tends to a ,find the value of (2-x/a)^tan(πx/2a)

Grade:12th pass

1 Answers

Snehal Jadhav
54 Points
5 years ago
The question is of the form 1infinity.
Such type of questions can be solved by using formula:
f(x)g(x) = e[f(x)-1]*g(x)
We, will evaluate e raised to the power:
(2 – (x/a) – 1)*tan(\pix/2a)
 
(1 – (x/a))*tan(\pix/2a)
 
((a – x)/a)*tan(\pix/2a)
Now, we will change the limits from x tends to a to (a+h) where, h tends to zero.
[(a – (a+h))/a]*tan(\pi(a+h)/2a)
 
[ – h/a]*[tan(\pi/2 + \pih/2a)
 
(-)h/a*(-)*(1/tan(\pih/2a))
 
h/a*(1/tan(\pih/2a))
The term tan(\pih/2a) tends to zero as h tends to zero.
So, tan(\pih/2a) equals to (\pih/2a).
Hence, the terms h and a cancel out.
2/h
So, the answer is:   e2/h

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