Approximate the area under the graph of $f(x)$ and above the $x$-axis with rectangles, using the following methods with $n=4$. \[ f(x)=e^{x}+2 \quad \text { from } x=-2 \text { to } x=2 \] (a) Use left endpoints. (b) Use right endpoints. (c) Average the answers in parts (a) and (b) (d) Use midpoints. The area, approximated using the left endpoints, is $\square$. (Round to two decimal places as needed.)

Step 1 ：We are asked to approximate the area under the curve of the function \(f(x) = e^x + 2\) from \(x=-2\) to \(x=2\) using rectangles. The number of rectangles to use is \(n=4\). For this part, we are using the left endpoints of each subinterval to determine the height of the rectangles.

Step 2 ：First, we need to determine the width of each rectangle. The total width of the interval is \(4\), so dividing this by the number of rectangles, we get a width of \(1\) for each rectangle.

Step 3 ：Next, we need to determine the height of each rectangle. Since we are using the left endpoints, the height of the rectangle on the \(i\)-th subinterval is \(f(x_i)\), where \(x_i\) is the left endpoint of the subinterval.

Step 4 ：The area of each rectangle is the width times the height, and the total area is the sum of the areas of all the rectangles.

Step 5 ：Let's calculate this. The left endpoints are \(-2, -1, 0, 1\). The corresponding heights are \(2.13533528, 2.36787944, 3, 4.71828183\). The areas of the rectangles are the same as the heights because the width is \(1\).

Step 6 ：The total area under the curve, approximated using the left endpoints and 4 rectangles, is approximately \(12.2214965528671\).

Step 7 ：Rounding this to two decimal places, we get \(12.22\).

Step 8 ：Final Answer: The area, approximated using the left endpoints, is \(\boxed{12.22}\).