Transcription of CONTINUITY AND DIFFERENTIABILITY
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CONTINUITY AND DIFFERENTIABILITY
Of a function at a pointLet f be a real function on a subset of the real numbers and let c be a point in thedomain of f. Then f is continuous at c iflim()()xcfxfc =More elaborately, if the left hand limit, right hand limit and the value of the functionat x = c exist and are equal to each other, ,lim()()lim()xcxcfxfcfx + ==then f is said to be continuous at x = in an interval(i)f is said to be continuous in an open interval (a, b) if it is continuous at everypoint in this interval.(ii)f is said to be continuous in the closed interval [a, b] if f is continuous in (a, b) limxa+ f (x) = f (a) limxb f (x) = f (b)Chapter5 CONTINUITY ANDDIFFERENTIABILITY20/04/2018 CONTINUITY AND DIFFERENTIABILITY meaning of CONTINUITY (i)Function f will be continuous at x = c if there is no break in the graph of thefunction at the point (),()cfc.
CONTINUITY AND DIFFERENTIABILITY 89 5.1.9 Chain rule is a rule to differentiate composition of functions. Let f = vou.If t = u (x) and both dt dx and dv dt exist then = . df dv dt dx dt dx 5.1.10 Following are some of the standard derivatives (in appropriate domains) 1. …
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