North South University MAT 250 MAT-250 mid term set 02
Answer any FIVE from the following:
1. Use polar coordinates to find the following limit:
lim
(?,?)→(0,0)
?2 + ?2
√?2 + ?2 + 1 - 1
2. Find an equation of the tangent plane and normal line to the surface ? = 16 - ?2 - ?2 at the point (2, 2, 8).
3. Find the directional derivative of ?(?, ?, ?) = ?3? - ??2 + ?2 at ?(2, -1, 1) in t
...[Show More]
North South University MAT 250 MAT-250 mid term set 02
Answer any FIVE from the following:
1. Use polar coordinates to find the following limit:
lim
(?,?)→(0,0)
?2 + ?2
√?2 + ?2 + 1 - 1
2. Find an equation of the tangent plane and normal line to the surface ? = 16 - ?2 - ?2 at the point (2, 2, 8).
3. Find the directional derivative of ?(?, ?, ?) = ?3? - ??2 + ?2 at ?(2, -1, 1) in the direction ? = 3? - ? + 2?.
4. Find the local maximum and minimum and the saddle points of ?(?, ?) = ?4 + ?4 - 4?? + 1.
5. Find the volume under the surface ? = ? cos ? cos2 ?? over the region ? = {(?, ?): 0 ≤ ? ≤ ?/2, 0 ≤ ? ≤ ?}.
6. Find the volume of the solid that lies under the paraboloid ? = ?2 + ?2 and above the region ? in the ??-plane
bounded by the line ? = 2? and the parabola ? = ?2.
[Show Less]