Evaluate ii) operatorname(Lim)(y) arrow(7) (2 y^2-11 y-21)/(2 y^2)-49

To evaluate the limit of the given expression as \( y \) approaches 7, we can substitute \( y = 7 \) directly into the expression:<br /><br />\[ \lim_{y \to 7} \frac{2y^2 - 11y - 21}{2y^2 - 49} \]<br /><br />Substituting \( y = 7 \):<br /><br />\[ \frac{2(7)^2 - 11(7) - 21}{2(7)^2 - 49} \]<br /><br />Simplify the numerator and denominator:<br /><br />\[ \frac{2(49) - 11(7) - 21}{2(49) - 49} \]<br /><br />\[ \frac{98 - 77 - 21}{98 - 49} \]<br /><br />\[ \frac{-21 + 98}{49} \]<br /><br />\[ \frac{49}{49} \]<br /><br />\[ 1 \]<br /><br />Therefore, the limit of the given expression as \( y \) approaches 7 is 1.