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Q: In Exercises 1–3, find a. v. u,| v|,|u| b. the cosine of the angle between v and u c. the scalar com...

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

Q: The question says: "Sketch the graph of a function for which f(0)=0, f'(0)=3, f'(1)=0, and f'(2)=-1....

A: Click to see the answer

Q: dy/dx of pi

A: pi is a constant.It has value 3.14 approx.

Q: In Exercises 1–2, find the length and direction (when defined) of u * v and v * u. 1. u =-8i - 2j - ...

A: find the length and direction (when defined) of u * v and v * u.

Q: What is the arc length function for a smooth parametrized curve? What is its arc length differential...

A: Click to see the answer

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: solve the following equation for X. 3*e^2x+7*e^x+2=0

A: Given,

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: describe the given set with a single equation or with a pair of equations.The set of points in space...

A: Let the points are given by (x,y,z)

Q: In Exercises 1–2, find a. v. u,| v|,|u| b. the cosine of the angle between v and u c. the scalar com...

A: given

Q: What are the Ratio and Root Tests? Do they always give you the information you need to determine con...

A: A mathematical series can be convergent or divergent subject to certain conditions. Ratio test and t...

Q: Identify and sketch the surfaces in Exercises 65–76. 65. x2 + y2 + z2 = 4 66. x2 + (y - 1)2 + z2 = 1...

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

Q: #1

A: Given differential equation and its solution is

Q: Find equations for the sphere whose centers and radii are given in center(0,-1,5) radius 2

A: Equation of sphere centered at (a, b, c) and having radius r is

Q: Find the lengths of the curves in Exercises 13–14. 13. y = x^1/2 - (1/3)x^3/2, 1<=x<= 4 14. x ...

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

Q: What is the Taylor series generated by a function ƒ(x) at a point x = a? What information do you nee...

A: With Taylor series, possible to guess what a function will look like in the area around the chosen p...

Q: if you have a parametric equation grapher, graph the equations over the given intervals x = 2 cos t ...

A: Click to see the answer

Q: In Exercises 33–34, find the distance from the point to the line. 33. (0, 0, 12); x = 4t, y =-2t, z ...

A: We’ll answer the 33th question since we answer only one question at a time. Please submit a new ques...

Q: In Exercises 1–4, let u = <-3, 4> and v = <2, -5>. Find (a) the component form of the ve...

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

Q: What geometric or physical interpretations do cross products have? Give examples.

A: Geometric or physical interpretations:The magnitude of the cross product of two vectors is the area ...

Q: If |v|= 2, |w|= 3, and the angle between v and w is pai/3, find | v - 2w|.

A: Given two vectors v and w with magnitudes 2 and 3 respectively and angle between them is pi/3

Q: What is the Integral Test? What is the reasoning behind it? Give an example of its use.

A: Click to see the answer

Q: Find parametric equations and a parameter interval for the motion of a particle starting at the poin...

A: Given,

Q: How can you sometimes find the area bounded by a parametrized curve and one of the coordinate axes?

A: Let the equation of parametrized curve be

Q: How do you find equations for lines, line segments, and planes in space? Give examples. Can you expr...

A: If you know two points (x1,y1,z1) and (x2, y2, z2) then to find the equation of a line you need the...

Q: Find an equation for the plane that passes through the point (3, -2, 1) normal to the vector n = 2i ...

A: Given:A point (3, -2, 1) normal to the vector n = 2i + j + kThe normal vector can be written as,

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: 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: A line segment of length a + b runs from the x-axis to the y-axis. The point P on the segment lies a...

A: Given A line segment of length a + b runs from the x-axis to the y-axis. The point P on the segment ...

Q: How can you tell when two planes A1 x + B1 y + C1 z = D1 and A2 x + B2 y + C2 z = D2 are parallel? P...

A: Two planes are parallel if their normal vectors are parallel.Normal vector of A1 x + B1 y + C1 z = D...

Q: Find an equation for the set of points equidistant from the point (0, 0, 2) and the x-axis.

A: To determine the equation for the set of the points.

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: What are the Taylor series for 1/(1 - x), 1/(1 + x), ex, sin x, cos x, ln (1 + x), and tan-1 x? How ...

A: Click to see the answer

Q: How do you graph equations in polar coordinates? Include in your discussion symmetry, slope, behavio...

A: Description:The polar equations are sketched in the polar coordinates by analysing the symmetrical s...

Q: What is a cylinder? Give examples of equations that define cylin-ders in Cartesian coordinates

A: Definition of cylinder:A closed solid that has two parallel bases connected by a curved surface is c...

Q: Calculate the derivative: y = sin2xln(sin22x)

A: The given function is,

Q: please solve and show your work

A: We have given the function f(x) = 6x - 3.

Q: Exercise 2: Determine the average value of the following functions, on the given interval. (a) x³, o...

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

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: Use Taylor’s formula with a = 0 and n = 3 to find the standard cubic approximation of ƒ(x) = 1/(1 - ...

A: The given function is,

Q: Exercise. The position vector for a particle is described by the vector-valued function: sin(at) r(t...

A: “Hey, since there are two questions posted, we will answer first question. If you want any specific ...

Q: In Exercises 29 and 30, find the distance from the point to the line. 29. (2, 2, 0); x =-t, y = t, z...

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

Q: Use the equation ƒ(x) = ƒ(a) + ƒ′(a)(x - a) + ƒ′′(c2) /2 (x - a)2 to establish the following test. L...

A: For the given function to determine its behaviour at a critical point x=a, use second derivative tes...

Q: What is a monotonic sequence? Under what circumstances does such a sequence have a limit? Give examp...

A: The monotonic sequence theorem:

Q: Find all real solutions of the ordinary differential equations: y''+4y=x

A: The general equation of the solution is,

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: How are vectors added and subtracted geometrically? Algebraically?

A: Vector Addition Geometrically:

Q: The line segment joining the points (0, 1) and (2, 2) is revolved about the x-axis to generate a fru...

A: The line segment joining the points (0, 1) and (2, 2) is revolved about the x-axis to generate a fru...