The limit $\lim _ { x \rightarrow - \infty } \frac { 4 - x } { x ^ { 2 } - 5 }$ is

A) $- \infty$
B) $\infty$
C) $- \frac { 4 } { 5 }$
D)0
E) $\frac { 4 } { 5 }$

Question

The limit $\lim _ { x \rightarrow - \infty } \frac { 4 - x } { x ^ { 2 } - 5 }$ is

A) $- \infty$
B) $\infty$
C) $- \frac { 4 } { 5 }$
D)0
E) $\frac { 4 } { 5 }$

Quizplus · Accepted Answer

When $x$ approaches $-\infty$, the degree of the polynomial in the denominator (which is 2) is higher than the degree of the polynomial in the numerator (which is 1). This means the value of the fraction approaches 0 as $x$ becomes very large in the negative direction.

The Limit lim⁡x→−∞4−xx2−5\lim _ { x \rightarrow - \infty } \frac { 4 - x } { x ^ { 2 } - 5 }limx→−∞​x2−54−x​

The Limit $\lim _ { x \rightarrow - \infty } \frac { 4 - x } { x ^ { 2 } - 5 }$