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 = 0
c. 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...
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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