a) Let the function f left parentheses x right parentheses equal 5 x raised to 4 plus 2 x cubed plus 5 x squared. Is it infinitesimal when x right arrow 0? Is it infinity when x right arrow 0? If it is one of those cases, calculate its order and its main part. When x right arrow infinity, is it an infinitesimal? And an infinity? If it is one of those cases, calculate its order and its main part. b) Analyze the character of the following integrals: integral subscript 5 superscript plus infinity end superscript fraction numerator 1 between denominator 5 x raised to 4 plus 2 x cubed plus 5 x squared end fraction dxy integral subscript 0 superscript plus infinity end superscript fraction numerator 1 between denominator 5 x raised to 4 more 2 x cubed plus 5 x squared end fraction dx
a) Let the function f left parentheses x right parentheses equal 5 x raised to 4 plus 2 x cubed plus 5 x squared. Is it infinitesimal when x right arrow 0? Is it infinity when x right arrow 0? If it is one of those cases, calculate its order and its main part. When x right arrow infinity, is it an infinitesimal? And an infinity? If it is one of those cases, calculate its order and its main part. b) Analyze the character of the following integrals: integral subscript 5 superscript plus infinity end superscript fraction numerator 1 between denominator 5 x raised to 4 plus 2 x cubed plus 5 x squared end fraction dxy integral subscript 0 superscript plus infinity end superscript fraction numerator 1 between denominator 5 x raised to 4 more 2 x cubed plus 5 x squared end fraction dx
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