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

54 Points
3 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($\pi$x/2a)

(1 – (x/a))*tan($\pi$x/2a)

((a – x)/a)*tan($\pi$x/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 + $\pi$h/2a)

(-)h/a*(-)*(1/tan($\pi$h/2a))

h/a*(1/tan($\pi$h/2a))
The term tan($\pi$h/2a) tends to zero as h tends to zero.
So, tan($\pi$h/2a) equals to ($\pi$h/2a).
Hence, the terms h and a cancel out.
2/h