Respuesta :
To find the oblique asymptote of the function ( f(x) = 2x^3 + 3x^2 + 4x + 5 ), we need to divide the function by the linear function ( y = ax + b ) using polynomial long division.The oblique asymptote will be ( y = 2x^2 + \frac{7}{a}x + \frac{5 + 4b}{a} ).For this to be an oblique asymptote, the linear term in the quotient (which is ( \frac{7}{a}x )) must match the linear term of the original function, which is ( 4x ).So, ( \frac{7}{a} = 4 ), which implies ( a = \frac{7}{4} ).Now, we can substitute ( a = \frac{7}{4} ) into the oblique asymptote equation to find the value of ( b ): [ b = \frac{5 + 4b}{a} = \frac{5 + 4b}{\frac{7}{4}} = \frac{20 + 16b}{7} ] [ 7b = 20 + 16b ] [ 9b = 20 ] [ b = \frac{20}{9} ]Now that we have ( a ) and ( b ), we can find ( \log_{16}^{-ab} ): [ ab = \frac{7}{4} \times \frac{20}{9} = \frac{35}{9} ][ \log_{16}^{-ab} = \log_{16}^{-\frac{35}{9}} ][ = \log_{16}{\left(\frac{1}{16^{\frac{35}{9}}}\
