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 . If)(xP)(xQax=is a common zero ofandthen the limit leads to the indeterminative )(xP)(xQ)(limxfax 00. This indeterminative may be eliminated by dividing bothandby the common factor)(xP)(xQax . Ex: Find 11lim21 xxx. D. Conjugate Radicals In same cases, to eliminate an indeterminative of the form 00we multiply both the numerator and denominator by a conjugate radical in order to cancel out a common zero.

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 …

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  Functions, Limits, Defined, Piecewise defined functions, Piecewise

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