Best George

10/12/2023 · Escuela secundaria superior

Question We are trying to prove the following limit. \[ \lim _{x \rightarrow-\infty}\left(\frac{4 x^{4}+7 x-1}{-6 x^{4}+9 x+5}\right)=-\frac{2}{3} \] One of the steps in the proof is to show that for every \( \varepsilon>0 \) there is a corresponding negative number \( N \) such that \[ \text { if } x<N, \text { then }|\square|<\varepsilon . \] Fill in the blank (shown as a square box) for this statement. Provide your answer below: If \( x<N \), then \( |\square|<\varepsilon \).