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Graph y = tan ( x ).
Solution
In the case of tangent we need to be careful while plugging x's in since tangent doesn't present wherever cosine is zero (remember that tan x = sin x/ cos x). Tangent will not preent at
x = ........, - 5 ∏/2 , - 3 ∏/2 , - ∏/2 , ∏ /2, 3 ∏/2 , 5 ∏/2 ,........
and at these pts the graph will have asymptotes. Following is the graph of tangent on the range - 5 ∏/2
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Verify Liouville''s formula for y "-y" - y'' + y = 0 in (0, 1) ?
x=ct,y=c/t d^2/dx^2
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