Identify and sketch the surfaces in Exercises 65–76. 65. x2 + y2 + z2 = 4 66. x2 + (y - 1)2 + z2 = 1 67. 4x2 + 4y2 + z2 = 4 68. 36x2 + 9y2 + 4z2 = 36 69. z =-(x2 + y2) 70. y =-(x2 + z2 )  71. x2 + y2 = z2 72. x2 + z2 = y2 73. x2 + y2 - z2 = 4 74. 4y2 + z2 - 4x2 = 4 75. y2 - x2 - z2 = 1 76. z2 - x2 - y2 = 1

Q: Most centroid calculations for curves are done with a calculator or computer that has an integral ev...

A:

Q: The vertices of an ellipse of eccentricity 0.5 lie at the points (0, +-2). Where do the foci lie?

A: The vertices of an ellipse of eccentricity is 0.5 lies on (0,+-2). Find the foci

Q: question 4

A: Hi there! Thank you for the question, but as per our guidelines we can solve only one question at a ...

Q: Find the perimeter of the triangle with vertices A(-1, 2, 1), B(1, -1, 3), and C(3, 4, 5).

A: Given:The vertices A(-1, 2, 1), B(1, -1, 3), and C(3, 4, 5).The perimeter of the triangle is AB + BC...

Q: Sketch the surfaces 1.z = 1 + y2 - x2  2. z =-(x2 + y2 ) 3. 4y2 + z2 - 4x2 = 4

A: Used graphing calculator to graph:z = 1 + y^2 - x^2 from two viewing angles

Q: Find parametric equations and a parameter interval for the motion of a particle that moves along the...

A:

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: f(x) =16 − x2, g(x) = x + 2 Find (f + g)(x)

A: Given functions are

Q: Find Taylor series at x = 0 for the functions  1/1 - 2x

A: The Taylor series expansion of a function f(x) at the point x = a can be written as

Q: Find the volume swept out by revolving the region bounded by the x-axis and one arch of the cycloid ...

A: Given:

Q: Let u, v, and w be vectors. Which of the following make sense, and which do not? Give reasons for yo...

A: a.

Q: give a geometric description of the set of points in space whose coordinates satisfy the given pairs...

A: Since you have asked multiple questions, we will solve the first question for you. If you want any s...

Q: a ball is thrown straight upwards from a tower ( 40 feet high) so thats its position, s in feet, t i...

A: Given:A ball is thrown straight upwards from a tower ( 40 feet high) so that’s its position, s in fe...

Q: Which polar coordinate pairs label the same point? a. (3, 0) b. (2, 7pai/3) c. (-3, 2pai) d. (-3, 0)...

A: a) (3,0)If we add pi with the angle then the radius will change its sign. So, (3,0) becomes (-3,0+pi...

Q: Exercises 45–48 give equations for parabolas and tell how many units up or down and to the right or ...

A: We’ll answer the first question (with complete information)  since the exact one wasn’t specified. P...

Q: Find the derivative of the following function g2 F(x) = ds a 3+ 5s4 using the appropriate form of th...

A: Given that,

Q: Find the angles between the planes in Exercises 47 and 48. 47. x + y = 1, 2x + y - 2z = 2 48. 5x + y...

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any s...

Q: Let a and b be constants with 0 < a < b. Does the sequence {(an + bn)}^1/n converge? If it doe...

A:

Q: Find parametric equations for the line in which the planes x + 2y + z = 1 and x - y + 2z =-8 interse...

A: x + 2y + z = 1 and x - y + 2z =-8 are the two planes.Let z=t So, the equations become: 

Q: Find the first four nonzero terms in the Maclaurin series for the functions in Exercises 31–38. 31. ...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Express the vectors in Exercises 9–10 in terms of their lengths and directions. 9. 22i + 22j  10. -i...

A: Since you have submitted two questions, we'll answer the first question. For the second question ple...

Q: The line segment joining the origin to the point (h, r) is revolved about the x-axis to generate a c...

A: Surface area formula of revolution about x axis is given by: 

Q: In Exercises 25–30, find the distance between points P1 and P2. 25. P1(1, 1, 1), P2(3, 3, 0) 26. P1(...

A: Given,

Q: Suppose that n is normal to a plane and that v is parallel to the plane. Describe how you would find...

A: Recall that the cross product of two vectors is perpendicular to both the vector. Given that the vec...

Q: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2, -...

A: Let <a,b,c> be the direction ratios of normal to plane , then the equation of he plane passing...

Q: According to the Alternating Series Estimation Theorem, how many terms of the Taylor series for tan-...

A: Taylor series expansion for tan-1x is given by,

Q: Find the binomial series for the functions in Exercises 11–13. 11. (1 + x)4 12. (1 - 2x)3  13. (1 + ...

A: As per our norms, I am going to solve only one question as you have posted multiple question so plea...

Q: In Exercises 37 and 38, find an equation for the plane through points P, Q, and R. 37. P(1, -1, 2), ...

A: Given, the points P(1, -1, 2), Q(2, 1, 3), R(-1, 2, -1)The vector

Q: a. Find the length of one arch of the cycloid x = a(t - sin t), y = a(1 - cos t). b. Find the area o...

A:

Q: Find the measures of the angles of the triangle whose vertices are A = (-1, 0), B = (2, 1), and C = ...

A: The given three vertices of a triangle are A(-1,0), B(2,1) and C(1,-2). Now, considering the sides o...

Q: Which of the following are always true, and which are not always true? Give reasons for your answers...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: Show that the line b2xx1 - a2yy1 - a2b2 = 0 is tangent to the hyperbola b2x2 - a2y2 - a2b2 = 0 at th...

A: Find dy/dx.Then find dy/dx at the point (x1,y1) by plugging x=x1 and y=y1

Q: Solve the differential equation listed below:

A: Separate the variables

Q: Find the areas of the surfaces generated by revolving the curves in Exercises 31–32 about the indica...

A: 31.The functions are,

Q: Give some typical parametrizations for lines, circles, parabolas, ellipses, and hyperbolas. How migh...

A: First of all, consider the cartesian form of the equation for the line.Then, consider the parametriz...

Q: A phone company charges $16.95 a month and 12 cents for every minute above 120 minutes. Write an exp...

A:  A phone company charges $16.95 a month and 12 cents for every minute above 120 minutes. Write an ex...

Q: How are integral tables typically used? What do you do if a particular integral you want to evaluate...

A: In simpler terms, the table of integrals offers readymade solution to different types of integral te...

Q: find a parametrization for the curve. 1. the line segment with endpoints (-1, -3) and (4, 1)

A:

Q: Find an equation for the plane that passes through the point (-1, 6, 0) perpendicular to the line x ...

A: Direction ratios of line x =-1 + t, y = 6 - 2t, z = 3t are  <1,-2,3> .Sine line is perpendicul...

Q: Find a plane through P0(2, 1, -1) and perpendicular to the line of intersection of the planes 2x + y...

A: The directional vectors of the planes are given by (2,1,-1) and (1,2,1)The directional vector of the...

Q: What is an infinite series? What does it mean for such a series to converge? To diverge? Give exampl...

A:

Q: Use the Taylor series for 1/ (1 - x2) to obtain a series for 2x/ (1 - x2)2.

A:

Q: describe the given set with a single equation or with a pair of equations.The circle of radius 1 cen...

A: Given,

Q: Exercises 53–54 give equations for hyperbolas and tell how many units up or down and to the right or...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Let u = i - 2j, v = 2i + 3j, and w = i + j. Write u = u1 + u2, where u1 is parallel to v and u2 is p...

A: u1 is parallel to v and u2 is parallel to w.So u1= av and u2=bwWhere a and b are constants.

Q: Find a formula for the distance from the point P(x, y, z) to the a. xy-plane . b. yz-plane c. zx-pla...

A: a) xy plane is given by z=0 We have to find distance of (x,y,z) from z=0 

Q: Find all real zeros of the function. g(x)=5(x2-36)(x-7)(x+7)2

A:

Q: use I=60/13(1-e-13t/5) to express the time t as a function of the current I

A: The given function of I as a function time t is as follows.

Q: How do you find a vector’s magnitude and direction?

A: If a vector is given. For example: ai+bj+ckThen to find the magnitude we need: 

Q: The ellipse (x2/9) + (y2/25) = 1 is shifted 3 units to the left and 2 units down to generate the ell...

A: Given,

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.