Transcription of 1.3 Limits (II) A. Piecewise-defined Functions
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1.3 Limits (II) A. Piecewise-defined Functions
Limits (II) A. Piecewise-defined Functions Let consider thatis a Piecewise-defined function: )(xf >=<=axxhaxcaxxgxf),(,),()( Then: )(lim)(limxgxfaxax =and )(lim)(limxhxfaxax++ =Ex: >+ =0,10,1)(2xxxxxf. Find . )(lim0xfx B. Algebraic Identities The following algebraic identities may be useful to find algebraically the limit of a function: oddnbbabaabababbabaababababbaabababababa babababababababannnnnnnnnnnn),..)(()..)( ())(())(())(())((12321123213223442233223 322 + +=+++++ = +++ = + +=+++ = + = C. Rational Functions Consider a rational function in the form: 0)(,)()()( =xQxQxPxfwhereandare polynomial Functions .
1.3 Limits (II) A. Piecewise-defined Functions Let consider that is a piecewise-defined function: f (x) h x x a c x a g x x a f x ( ),, ( ), ( ) 1 Then: lim f (x) lim g(x) x→a− x→a− = and lim f (x) lim h(x) x→a+ x→a+ Ex:
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