Use l'H^opital's rule to find the limit.
-$\lim _ { x \rightarrow \infty } \frac { 7 x ^ { 2 } - 5 x + 1 } { 3 x ^ { 2 } + 3 x - 8 }$
A) $\frac { 7 } { 3 }$
B) $\infty$
C) 7
D) 1

Question

Quizplus · Accepted Answer

Applying l'Hopital's rule, we take the derivative of the numerator and denominator separately (since they are both polynomials of degree 2) and evaluate the limit again:

\begin{align*} \lim_{x	o\infty}\frac{7x^2-5x+1}{3x^2+3x-8} &= \lim_{x	o\infty}\frac{14x-5}{6x+3} \ &= \lim_{x	o\infty}\frac{14}{6} \ &= \frac{7}{3} \end{align*}

Therefore, the answer is A, $\frac{7}{3}$.

Use L'H^opital's Rule to Find the Limit lim⁡x→∞7x2−5x+13x2+3x−8\lim _ { x \rightarrow \infty } \frac { 7 x ^ { 2 } - 5 x + 1 } { 3 x ^ { 2 } + 3 x - 8 }limx→∞​3x2+3x−87x2−5x+1​

Use L'H^opital's Rule to Find the Limit $\lim _ { x \rightarrow \infty } \frac { 7 x ^ { 2 } - 5 x + 1 } { 3 x ^ { 2 } + 3 x - 8 }$