Find, $\lim _{x \rightarrow \infty} \frac{4 x^{7}-3 x+2}{11 x^{7}+100 x-5}$
if it exists.
A)1
B) $\frac{4}{11}$

C) $\frac{7}{11}$
D)DNE
E) $\frac{-2}{5}$

Question

Find, $\lim _{x \rightarrow \infty} \frac{4 x^{7}-3 x+2}{11 x^{7}+100 x-5}$
 if it exists.
A)1
B) $\frac{4}{11}$

C) $\frac{7}{11}$
D)DNE
E) $\frac{-2}{5}$

Quizplus · Accepted Answer

To find the limit of a rational function as $x$ approaches infinity, divide every term by the highest power of $x$ present in the denominator, which in this case is $x^7$. This simplifies the expression to $\frac{4 - 3/x^6 + 2/x^7}{11 + 100/x^6 - 5/x^7}$. As $x$ approaches infinity, the terms with $x$ in the denominator approach 0, leaving $\frac{4}{11}$ as the limit.

Find lim⁡x→∞4x7−3x+211x7+100x−5\lim _{x \rightarrow \infty} \frac{4 x^{7}-3 x+2}{11 x^{7}+100 x-5}limx→∞​11x7+100x−54x7−3x+2​ If It Exists

Find $\lim _{x \rightarrow \infty} \frac{4 x^{7}-3 x+2}{11 x^{7}+100 x-5}$ If It Exists