1.
A solid in the first octant, bounded by the coordinateplanes, the plane (x= 40) and the curve (z=1-y² ) , Find the volumeof the solid by using : a- Double integration technique ( Use orderdy dx) b-Triple integration technique ( Use order dz dydx)
2.
Use triple integration in Cartesian coordinates tofind the volume of the solid that lies below the surface = 16 − ?²− ?² , above the plane z = 40/ 100 , and bounded by the curve ? =√? and the lines ? = ? − 2 and ? = −?.
3.
Find all the local maxima, local minima, and saddlepoints of the function ?(?, ?) = 40?² − 2?³ + 3?² + 6?y
4.
Let ? = ? − sin(??) ?ℎ??? ? = 40? ? = ln(?) ? =e^(t-1)Find ??/?? by :- a- Using Chain Rule principles
b- Expressing (?) in term of (?) then differentiating directly
5.
a- Use implicit differentiation to find (d²y)/(dx² )of the following curve at the point (π, 2π).y² = x²+ sin?y
b- Show that ?âµ?⧸ ??²??³ is zero in twodifferentiation steps only. ?(?, ?) = ??^ ?²/â´â°
Ù…Øمد مهدي جميل ?, [â§ÙŠÙˆÙ†ÙŠÙˆ â¨30â©ØŒ â¨2020â© ÙÙŠ â¨18:22â©â©]
Show that ?�/ ??²??³ is zero in three differentiation steps only.?(?, ?) = ?² + ?(sin ? – ?ⴠ).
