let f(x): x2 sin(l/x) for 0 Solution f(x) = (x^2) * sin(1/x) ...................

ID: 2979727 • Letter: L

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let f(x): x2 sin(l/x) for 0

Explanation / Answer

f(x) = (x^2) * sin(1/x) .................................................................................................................................................... lt x-> 0 f(x) = lt x->0 (x^2) * sin(1/x) .................................................................................................................................................... since, sine function value varies from -1 to 1 , x^2 -> 0 as x->0 ..................................................................................................................................................... therefore, sin(1/x) lies between -1 to 1 ..................................................................................................................................................... therefore, lt x->0 (x^2)*sin(1/x) = 0 ...................................................................................................................................................... g(x) = x^2 ...................................................................................................................................................... lt x->0 g(x) = lt x->0 x^2 = 0 , as x->0 then x^2 -> 0 ..................................................................................................................................................... lt x->0 f(x)/g(x) = lt x->0 sin(1/x) = some value but not known, ...................................................................................................................................................... since sin(infinity) is not zero but lies between -1 and 1. ..................................................................................................................................................... therefore, lt x-> 0 f(x) = lt x->0 g(x) = lt x->0 f(x)/g(x) doesnot exist

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let f(x): x2 sin(l/x) for 0 Solution f(x) = (x^2) * sin(1/x) ...................

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