Divide numerator and denominator by the highest power of x in the denominator to find the limit.
-$$\lim _ { x \rightarrow \infty } \sqrt { \frac { 25 x ^ { 2 } + x - 3 } { ( x - 11 ) ( x + 1 ) } }$$
A) 0
B) 25
C) $\infty$
D) 5

Question

Quizplus · Accepted Answer

The highest power of x in the denominator is x. Dividing numerator and denominator by x, we get
$$\lim _ { x \rightarrow \infty } \sqrt { \frac { 25 + \frac { 1 } { x } - \frac { 3 } { x ^ { 2 } } } { ( 1 - \frac { 11 } { x } ) ( 1 + \frac { 1 } { x } ) } } = \lim _ { x \rightarrow \infty } \sqrt { \frac { 25 + 0 + 0 } { 1 \cdot 1 } } = \boxed{5}$$

Divide Numerator and Denominator by the Highest Power of X lim⁡x→∞25x2+x−3(x−11)(x+1)\lim _ { x \rightarrow \infty } \sqrt { \frac { 25 x ^ { 2 } + x - 3 } { ( x - 11 ) ( x + 1 ) } }x→∞lim​(x−11)(x+1)25x2+x−3​​

Divide Numerator and Denominator by the Highest Power of X $\lim _ { x \rightarrow \infty } \sqrt { \frac { 25 x ^ { 2 } + x - 3 } { ( x - 11 ) ( x + 1 ) } }$