Complete the table and use the result to estimate the limit. $\lim _ { x \rightarrow 7 } \frac { \frac { 1 } { x - 3 } - \frac { 1 } { 4 } } { x - 7 }$
$\begin{array}{|c|c|c|c|c|c|c|}
\hline x & 6.9 & 6.99 & 6.999 & 7.001 & 7.01 & 7.1 \
\hline f(x) & & & & & & \
\hline
\end{array}$

A) $- 0.062500$
B) $0.067500$
C) $- 0.192500$
D) $0.047500$
E) $- 0.172500$

Question

Complete the table and use the result to estimate the limit. $\lim _ { x \rightarrow 7 } \frac { \frac { 1 } { x - 3 } - \frac { 1 } { 4 } } { x - 7 }$
$\begin{array}{|c|c|c|c|c|c|c|}
\hline x & 6.9 & 6.99 & 6.999 & 7.001 & 7.01 & 7.1 \
\hline f(x) & & & & & & \
\hline
\end{array}$

A) $- 0.062500$
B) $0.067500$
C) $- 0.192500$
D) $0.047500$
E) $- 0.172500$

Quizplus · Accepted Answer

To estimate the limit, we can substitute the values of $x$ into the function and observe the trend as $x$ approaches 7. The correct choice is based on the calculation of the limit, which yields $-0.062500$. This is derived from simplifying the expression and evaluating the limit analytically, which involves algebraic manipulation and applying the limit laws.

Complete the Table and Use the Result to Estimate the Limit