Which of the following are always true, and which are not always true? Give reasons for your answers.a. u .u = |u |b. u * 0 = 0 * u = 0c. u * (-u) = 0

Q: What are the basic facts about a. sums, differences, and products of power series? b. substitution o...

A: (a) The basic facts about sums, differences, and products of power series.

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

A: First graph the situation  

Q: Find the center C and the radius a for the spheres in Exercises 51–52. 51. x2 + y2 + z2 - 6y + 8z = ...

A: We’ll answer the 51th question since we answer only one question at a time. Please submit a new ques...

Q: The circles r = sqrt(3) cos u and r = sin u intersect at the point (sqrt(3)/2, pai/3). Show that the...

A: For r=sqrt(3)cos(theta) find dr/d theta 

Q: Exercises 17–20 give equations for ellipses. Put each equation in standard form. Then sketch the ell...

A: Note: We’ll answer the 17th question since we answer only one question at a time. Please submit a ne...

Q: What is a reduction formula? How are reduction formulas used? Give an example.

A: Reduction formulae are integrals involving some variable n.Given the one reduction formula: 

Q: What theorem sometimes enables us to use l’Hôpital’s Rule to calculate the limit of a sequence? Give...

A: The theorem which enables us to use L'Hospital’s Rule  is,

Q: If u and v are orthogonal, show that projv u = 0.

A: If u and v are orthogonal, show that projv u = 0

Q: What are the standard equations for lines and conic sections in polar coordinates? Give examples.

A: The standard polar equation for lines is given by