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Differential Calculus> May get help proving this one....

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May get help proving this one.

Gribesh Dhakal , 10 Years ago

Grade 11

1 Answers

Riddhish Bhalodia

put a-x =t and we get
$L = lim_{t\rightarrow\infty}t\times tan(\pi/2 - \pi t/2a) = lim_{t\rightarrow\infty}t\times cot( \pi t/2a)$
now by writing cot in terms of sin and cos we can just take out the cos as cos(0) = 1, and hence what remains is
$L = lim_{t\rightarrow\infty}\frac{t}{sin(\pi t/2a)} = (2a/\pi)lim_{t\rightarrow\infty}\frac{\pi t/2a}{sin(\pi t/2a)}$
and we know that the form oflimit x/sin(x) as x->0 is 1
hence proved
$L = (2a/\pi)$

Last Activity: 10 Years ago

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