Repaso del contenido impartido II

El método de evaluación sirve para determinar frente a qué tipo de indeterminación me encuentro.

$stack l i m with x rightwards arrow 3 below fraction numerator x squared minus 9 over denominator x minus 3 end fraction equals stack l i m with x rightwards arrow 3 below space fraction numerator 3 squared minus 9 over denominator 3 minus 3 end fraction equals stack l i m with x rightwards arrow 3 below space fraction numerator 9 minus 9 over denominator 3 minus 3 end fraction equals fraction numerator 9 minus 9 over denominator 3 minus 3 end fraction equals 0 over 0 I n d e t e r m i n a c i o n space d e l space t i p o space 0 over 0 stack l i m with x rightwards arrow 1 below fraction numerator 6 x squared plus 12 x space minus space 18 over denominator 2 x minus 2 end fraction equals stack l i m with x rightwards arrow 1 below fraction numerator 6 left parenthesis 1 right parenthesis squared plus 12 left parenthesis 1 right parenthesis space minus space 18 over denominator 2 left parenthesis 1 right parenthesis minus 2 end fraction equals fraction numerator 6 plus 12 space minus space 18 over denominator 2 minus 2 end fraction equals fraction numerator 18 space minus space 18 over denominator 2 minus 2 end fraction equals 0 over 0 I n d e t e r m i n a c i o n space d e l space t i p o space 0 over 0 stack l i m with x rightwards arrow 3 below space open parentheses 3 minus x close parentheses x over open parentheses x minus 3 close parentheses cubed equals stack l i m with x rightwards arrow 3 below space open parentheses 3 minus 3 close parentheses 3 over open parentheses 3 minus 3 close parentheses cubed equals stack l i m with x rightwards arrow 3 below space open parentheses 0 close parentheses 3 over open parentheses 0 close parentheses cubed equals open parentheses 0 close parentheses fraction numerator 3 over denominator open parentheses 0 close parentheses end fraction equals 0 cross times infinity I n d e t e r m i n a c i o n space d e l space t i p o space 0 cross times infinity space$

$f left parenthesis x right parenthesis equals fraction numerator x plus 3 over denominator x squared minus 25 end fraction space minus space fraction numerator x over denominator x minus 5 end fraction stack l i m with x rightwards arrow 5 below space f left parenthesis x right parenthesis equals stack l i m with x rightwards arrow 5 below space fraction numerator x plus 3 over denominator x squared minus 25 end fraction space minus space fraction numerator x over denominator x minus 5 end fraction equals stack l i m with x rightwards arrow 5 below space fraction numerator 5 plus 3 over denominator 5 squared minus 25 end fraction space minus space fraction numerator 5 over denominator 5 minus 5 end fraction equals stack l i m with x rightwards arrow 5 below space 8 over 0 space minus space 5 over 0 stack l i m with x rightwards arrow 5 below space 8 over 0 space minus space 5 over 0 equals 8 over 0 space minus space 5 over 0 equals infinity minus infinity I n d e t e r m i n a c i o n space d e l space t i p o space infinity minus infinity. h left parenthesis x right parenthesis equals square root of x squared plus 3 x end root space minus space x stack l i m with x rightwards arrow infinity below h left parenthesis x right parenthesis equals stack l i m with x rightwards arrow infinity below space space square root of x squared plus 3 x end root space minus space x equals space stack l i m with x rightwards arrow infinity below space space square root of left parenthesis infinity right parenthesis squared plus 3 left parenthesis infinity right parenthesis end root space minus space left parenthesis infinity right parenthesis equals infinity minus infinity. I n d e t e r m i n a c i o n space d e l space t i p o space infinity minus infinity.$