00:01
Hi, in this question we need to find the given surface area.
00:04
Here, given that, z equal to 5 minus x squared minus y square, where 1 less than are equal to z less than or equal to 4, and also f of x comma y comma z equals x squared divided by 5 minus z.
00:21
First we need to differentiate with respect to x.
00:25
So, z x equals minus 2x and z z.
00:31
Equals minus 2y.
00:34
On substituting z -equal to 1, then we get x squared plus y -square equal to 4.
00:41
On substituting z -equal to 4, then we get x -square plus y -square equal to 1.
00:47
Next, we need to consider x -equal to r -cost -theta and y -equal to r -syn theta.
00:56
And also we know that x -square plus y -square equal to r -square.
01:02
Here r lies between 1 and 2, so 1 less than r less than 2 and theta lies between 0 less than theta less than 2 pi...