Calculate the limit algebraically.
$\lim _ { x \rightarrow + \infty } \frac { 7 x ^ { 2 } + 7 x - 6 } { 10 x ^ { 2 } - 2 }$
A) $- \frac { 1 } { 2 }$
B) $\frac { 9 } { 10 }$
C) $\frac { 7 } { 10 }$
D) $\frac { 1 } { 11 }$
E) $\frac { 1 } { 10 }$

Question

Calculate the limit algebraically.  
  $\lim _ { x \rightarrow + \infty } \frac { 7 x ^ { 2 } + 7 x - 6 } { 10 x ^ { 2 } - 2 }$  
A) $- \frac { 1 } { 2 }$
B)   $\frac { 9 } { 10 }$
C)   $\frac { 7 } { 10 }$
D)   $\frac { 1 } { 11 }$
E)   $\frac { 1 } { 10 }$

Quizplus · Accepted Answer

To find the limit as $x$ approaches infinity, divide every term by $x^2$, the highest power of $x$ in the expression. This gives $\lim _ { x \rightarrow + \infty } \frac { 7 + \frac{7}{x} - \frac{6}{x^2} } { 10 - \frac{2}{x^2} }$. As $x$ approaches infinity, the terms $\frac{7}{x}$, $\frac{6}{x^2}$, and $\frac{2}{x^2}$ approach 0, leaving $\frac{7}{10}$.

Calculate the Limit Algebraically lim⁡x→+∞7x2+7x−610x2−2\lim _ { x \rightarrow + \infty } \frac { 7 x ^ { 2 } + 7 x - 6 } { 10 x ^ { 2 } - 2 }limx→+∞​10x2−27x2+7x−6​

Calculate the Limit Algebraically $\lim _ { x \rightarrow + \infty } \frac { 7 x ^ { 2 } + 7 x - 6 } { 10 x ^ { 2 } - 2 }$