Complete the table for the function $y = \sqrt { x }$ . Let x = 4. $\begin{array} { l }
d x=\Delta x \quad d y \quad \Delta y \quad \Delta y-d y \quad d y / \Delta y\
1.00000 \
0.50000 \
0.10000
\end{array}$
A) $\begin{array} { l l l l l }
d x = \Delta x & d y & \Delta y & \Delta y - d y & d y / \Delta y \
1.00000 & 0.25 & 0.23607 & - 0.01393 & 1.05901 \
0.50000 & 0.125 & 0.12132 & - 0.00368 & 1.03033 \
0.10000 & - 0.0061 & 0.02485 & - 0.00015 & 1.00825
\end{array}$
B) $\begin{array} { l l l l l }
d x = \Delta x & d y & \Delta y & \Delta y - d y & d y / \Delta y \
1.00000 & 0.25 & 0.23607 & - 0.01393 & 1.05901 \
0.50000 & 0.125 & 0.43132 & - 0.00368 & 1.03454 \
0.10000 & 0.025 & 0.02485 & - 0.00015 & 1.00604
\end{array}$
C) $\begin{array} { l l l l l }
d x = \Delta x & d y & \Delta y & \Delta y - d y & d y / \Delta y \
1.00000 & 0.3011 & 0.23607 & - 0.01393 & 1.05901 \
0.50000 & 0.125 & 0.43132 & - 0.00368 & 1.03454 \
0.10000 & - 0.0061 & 0.02485 & - 0.00015 & 1.00825
\end{array}$
D) $\begin{array} { l l l l l }
d x = \Delta x & d y & \Delta y & \Delta y - d y & d y / \Delta y \
1.00000 & 0.3011 & 0.23607 & - 0.01393 & 1.05901 \
0.50000 & 0.125 & 0.12132 & - 0.00368 & 1.03033 \
0.10000 & - 0.0061 & 0.02485 & - 0.00015 & 1.00825
\end{array}$
E) $\begin{array} { l l l l l }
d x = \Delta x & d y & \Delta y & \Delta y - d y & d y / \Delta y \
1.00000 & 0.25 & 0.23607 & - 0.01393 & 1.05901 \
0.50000 & 0.125 & 0.12132 & - 0.00368 & 1.03033 \
0.10000 & 0.025 & 0.02485 & - 0.00015 & 1.00604
\end{array}$

Question

Complete the table for the function $y = \sqrt { x }$ . Let x = 4. $\begin{array} { l } 
d x=\Delta x \quad d y \quad \Delta y \quad \Delta y-d y \quad d y / \Delta y\
1.00000 \
0.50000 \
0.10000
\end{array}$
A) $\begin{array} { l l l l l } 
d x = \Delta x & d y & \Delta y & \Delta y - d y & d y / \Delta y \
1.00000 & 0.25 & 0.23607 & - 0.01393 & 1.05901 \
0.50000 & 0.125 & 0.12132 & - 0.00368 & 1.03033 \
0.10000 & - 0.0061 & 0.02485 & - 0.00015 & 1.00825
\end{array}$
B) $\begin{array} { l l l l l } 
d x = \Delta x & d y & \Delta y & \Delta y - d y & d y / \Delta y \
1.00000 & 0.25 & 0.23607 & - 0.01393 & 1.05901 \
0.50000 & 0.125 & 0.43132 & - 0.00368 & 1.03454 \
0.10000 & 0.025 & 0.02485 & - 0.00015 & 1.00604
\end{array}$
C) $\begin{array} { l l l l l } 
d x = \Delta x & d y & \Delta y & \Delta y - d y & d y / \Delta y \
1.00000 & 0.3011 & 0.23607 & - 0.01393 & 1.05901 \
0.50000 & 0.125 & 0.43132 & - 0.00368 & 1.03454 \
0.10000 & - 0.0061 & 0.02485 & - 0.00015 & 1.00825
\end{array}$
D) $\begin{array} { l l l l l } 
d x = \Delta x & d y & \Delta y & \Delta y - d y & d y / \Delta y \
1.00000 & 0.3011 & 0.23607 & - 0.01393 & 1.05901 \
0.50000 & 0.125 & 0.12132 & - 0.00368 & 1.03033 \
0.10000 & - 0.0061 & 0.02485 & - 0.00015 & 1.00825
\end{array}$
E) $\begin{array} { l l l l l } 
d x = \Delta x & d y & \Delta y & \Delta y - d y & d y / \Delta y \
1.00000 & 0.25 & 0.23607 & - 0.01393 & 1.05901 \
0.50000 & 0.125 & 0.12132 & - 0.00368 & 1.03033 \
0.10000 & 0.025 & 0.02485 & - 0.00015 & 1.00604
\end{array}$

Quizplus · Accepted Answer

The correct values for $d y$ are calculated based on the derivative of $y = \sqrt{x}$ at $x = 4$, which is $\frac{1}{2\sqrt{x}}$. For $\Delta x = 1, 0.5, 0.1$, the corresponding $d y$ values are calculated using this derivative, and $\Delta y$ is the actual change in $y$ values from $y = \sqrt{x}$ to $y = \sqrt{x + \Delta x}$. The choice E accurately reflects these calculations and the correct application of the derivative for small changes in $x$.

Complete the Table for the Function y=xy = \sqrt { x }y=x​

Complete the Table for the Function $y = \sqrt { x }$