1. Formula: \[ =VLOOKUP(B1, B4 : D6, 2, 0) \]
Reason: The reference range used in this formula (B4:D6) does not include the entire data set. The range should start from the top row of the table (e.g., B1:D7) for proper referencing.
2. Formula: \[ =SQRT(VLOOKUP(C2, C2 : D8, 2, 0) - 100) \]
Reason: The VLOOKUP function is trying to search for the value in C2 within the range C2:D8, which results in an invalid range. The lookup value should exist within a different range.
3. Formula: \[ =VLOOKUP(B5, B6 : D8, 1, 0) \]
Reason: The 1st column index (A) does not exist in the lookup range (B6:D8). The first column should be in the lookup range for the formula to work properly.
4. Formula: \[ =VLOOKUP(B3, B2 : D5, 5, 0) \]
Reason: The column index (5) exceeds the available columns in the specified range (B2:D5). The column index should be less than or equal to the number of columns in the range.
5. Formula: \[ =VLOOKUP(B5, B3 : D8, 0) \]
Reason: The column index (0) is invalid. The column index must be a positive integer that corresponds to a column number within the given range.
6. Formula: \[ =VLOOKUP(B2, B2 : D7, 2, 0) \]
Reason: This error occurs if the lookup value (B2) does not exist in the first column of the specified range. Ensure the lookup value is available in the range for a correct lookup.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).