Multiple Integrals - Volume of a drilled space in a sphere

I have enclosed all details on the attached file. How do I find the volume of the drilled area? Consider a sphere of radius R and circular hole 2d drilled through along axis of symmetry...

Multiple Integrals : Volume of a Sphere with a Hole Drilled Through it

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Find the differential equations of all parabolas whose axes are parallel to the y-axis.

Find the differential equations of all parabolas whose axes are parallel to the axis of y.

How do you prove on the basis of the definition, the function f defined by f(x,y)=xy(x+y) is differentiable at every point of its domain?

My definition goes: If the function has its derivatives at point (a,b) then the function is differentible at (a,b) How do you prove on the basis of the definition, the function f defined by f(x,y)=xy(x+y) is differentiable at every point of its domain?

Two-Sided Limits : g(x,y)=｜x｜y (that's module sign) prove that g is not differentiable at (0,b) for any value non-zero value of b.

g(x,y)=｜x｜y (that's module sign) prove that g is not differentiable at (0,b) for any value non-zero value of b.

Change of Variables

Show that the change of variables.... Reduces 21.1 to the simpler and more familiar form from Ch. 18 Greenberg text, change of variables Please see the attached file for the fully formatted problems.

Differential equations by systematic elimination

I could use your assistance with a problem. The problem is to be soulved by using MATLAB. I have the stu version 6.0. I'm not real familure with using it, if you could show me the code on the problem I would greatly appriciate it. I have tried for a long time with no headway. I'm sorry, I wrote the problem in complete. t ...continues

Fundamental set of solutions of a Differential Equation : Verify that e^x Cos(2x) and e^x Sin(2x) form a fundamental set of solutions of the differential equation [ y'' - 2y + 5y = 0 ] on the ...

Verify that e^x Cos(2x) and e^x Sin(2x) form a fundamental set of solutions of the differential equation [ y'' - 2y + 5y = 0 ] on the interval (- infinity, infinity). With the e^x the "x" is the only upper score in the problem. The Cos and Sin are on the regular line of the problem.

Simplifying and 'Together and Alone' Type Word Problems

12. Simplify: 10 t^6 3 ---- - --- -:- ---- t^2 2 t^5 13. Add: 4 7 ---- + ---- X x^2 14. Sandra can paint a kitchen in 5 hours and James can paint the same kitchen in 6 hours. How long would it take them working toget ...continues

Partial Differential Equations : Separation Solutions, Initial Conditions, Boundary Conditions and Boundary Value Problems

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