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Differential Calculus> Help Please...

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Help Please

Gribesh Dhakal , 10 Years ago

Grade 11

1 Answers

Riddhish Bhalodia

We start with substituting x = a + t, and hence as x tends to a, t tends to 0. so the limit now becomes
$L = lim_{t\rightarrow 0} (-t)tan(\frac{\pi}{2}(1 + \frac{t}{a})) = lim_{t\rightarrow 0} tcot(\frac{\pi t}{2a})$
this can be written in form of standard limit multiples as
$L = lim_{t\rightarrow 0} cos(\frac{\pi t}{2a})\frac{\frac{\pi t}{2a}}{sin(\frac{\pi t}{2a})} \frac{2a}{\pi}$
now as per the standard limit rules the limits of the first two factos is 1 and hence
$L = \frac{2a}{\pi}$
Proved!

Last Activity: 10 Years ago

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