lim _(xarrow infty )(5x^3+3x-4)/(x^3)+1 angering theorem (sandwich theorem b) lim _(xarrow infty )(x^2+3)/(x^5)+1 c) lim _(xarrow infty )(3x)/(sqrt (16x^2)+3)

a) To find the limit of the given expression as x approaches infinity, we can use the fact that the limit of a rational function as x approaches infinity is equal to the ratio of the leading coefficients of the numerator and denominator.<br /><br />In this case, the leading coefficient of the numerator is 5 and the leading coefficient of the denominator is 1. Therefore, the limit of the given expression as x approaches infinity is 5.<br /><br />b) To find the limit of the given expression as x approaches infinity, we can use the fact that the limit of a rational function as x approaches infinity is equal to the ratio of the leading coefficients of the numerator and denominator.<br /><br />In this case, the leading coefficient of the numerator is 1 and the leading coefficient of the denominator is 1. Therefore, the limit of the given expression as x approaches infinity is 0.<br /><br />c) To find the limit of the given expression as x approaches infinity, we can use the fact that the limit of a rational function as x approaches infinity is equal to the ratio of the leading coefficients of the numerator and denominator.<br /><br />In this case, the leading coefficient of the numerator is 3 and the leading coefficient of the denominator is 4. Therefore, the limit of the given expression as x approaches infinity is 3/4.