Find the limit (if it exists). $\lim _ { x \rightarrow \infty } \left( \frac { 5 - 40 x } { x + 5 } \right)$
A)40
B)-40
C)5
D)-8
E)does not exist

Question

Find the limit (if it exists).  $\lim _ { x \rightarrow \infty } \left( \frac { 5 - 40 x } { x + 5 } \right)$ 
A)40
B)-40
C)5
D)-8
E)does not exist

Quizplus · Accepted Answer

To find the limit as $x$ approaches infinity for the given expression, divide every term in the numerator and the denominator by $x$, the highest power of $x$ in the denominator. This yields $\lim _ { x \rightarrow \infty } \left( \frac { 5/x - 40 } { 1 + 5/x } \right)$. As $x$ approaches infinity, $5/x$ and $5/x$ in the numerator and denominator respectively approach 0, simplifying the expression to $-40$.

Find the Limit (If It Exists) lim⁡x→∞(5−40xx+5)\lim _ { x \rightarrow \infty } \left( \frac { 5 - 40 x } { x + 5 } \right)limx→∞​(x+55−40x​)

Find the Limit (If It Exists) $\lim _ { x \rightarrow \infty } \left( \frac { 5 - 40 x } { x + 5 } \right)$