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Continuity And Differentiability

Question

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Examine whether the function f given by f(x) = x² is continuous at x = 0.

Solution

Here space space straight f left parenthesis straight x right parenthesis equals straight x squared Lt with straight x rightwards arrow 0 below space straight f left parenthesis straight x right parenthesis equals Lt with straight x rightwards arrow 0 below space straight x squared equals left parenthesis 0 right parenthesis squared equals 0 Now space straight f space is space defined space at space straight x equals 0 and space straight f left parenthesis 0 right parenthesis equals 0 therefore stack Lt space with straight x rightwards arrow 0 below straight f left parenthesis straight x right parenthesis equals straight f left parenthesis 0 right parenthesis equals 0 therefore space straight f space is space continous space at space straight x equals 0.

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