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Q: By multiplying the Taylor series for ex and sin x, find the terms through x5 of the Taylor series fo...

A: First, we need to find the terms through x5 of the Taylor series for ex sin x which is found by mul...

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: In Exercises 1–3, give a geometric description of the set of points in space whose coordinates satis...

A: Given,

Q: Express in terms of sums and differences of logarithms

A: According to the given information it is required to write the expression in terms of sum and differ...

Q: Express the vectors in Exercises 9–10 in terms of their lengths and directions. 9. Velocity vector v...

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

Q: In Exercises 1–5, find the length and direction (when defined) of u * v and v * u. 1. u = 2i - 2j - ...

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

Q: Show that the number 4p is the width of the parabola x2 = 4py (p>0) at the focus by showing that ...

A: Click to see the answer

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

A: Given,

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: A bacteria culture starts with 300 bacteria and doubles in size every half hour. (a) How many bacter...

A: Click to see the answer

Q: if you have a parametric equation grapher, graph the equations over the given intervals a. x = 6 cos...

A: If instead of usual form of y = f(x), where y is dependent upon variable x, Suppose both x and y are...

Q: What is the limit?

A: Limit x->2 means x is approaching 2.So plug x=2 in the given expression.

Q: What geometric interpretation does the dot product have? Give examples.

A: The geometrical interpretation of the dot product of u.v is the length of the projection of the vect...

Q: Find the rules for the composite functions f ∘ g and g ∘ f. f(x)=square root of (x+9) and g(x)= 1...

A: fog means f(g(x))We plug g(x)=1/(x-9) inside f(x).Then replace x in f(x) by 1/(x-9) to find f(1/(x-9...

Q: What is the second derivative of the function: f(x) = (9x^2)/ (x^2-49) Please show ALL steps

A: Given function is

Q: Find the center C and the radius a for the spheres in Exercises 51–52. 51. (x + 2)2 + y2 + (z - 2)2 ...

A: To determine the centre and radius of the sphere.

Q: Use similar triangles to find the coordinates of the point Q that divides the segment from P1(x1, y1...

A: Given:

Q: Let u = i + 2j - k, v =-i + j + k, w = i + k, r =-(pa/i2)i - pai j + (pai/2)k. Which vectors, if any...

A: Given:

Q: To illustrate the fact that the numbers we get for length do not depend on the way we parametrize ou...

A: Given,

Q: Find a 2 * 2 determinant formula for the area of the triangle in the xy-plane with vertices at (0, 0...

A: Given, vertices of the triangle are

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

A: a) False

Q: Solve the differential equation listed below:

A: Separate the variables

Q: Find parametric equations and a parameter interval for the motion of a particle that starts at the p...

A: Given that the motion of a particle that starts at the point (-2, 0) in the xy-plane and traces the ...

Q: Let u = 5i - j + k, v = j - 5k, w =-15i + 3j - 3k. Which vectors, if any, are (a) perpendicular? (b)...

A: To determine the vector which are,Part (a) ParallelPart (b) Perpendicular

Q: Find equations for the planes in Exercises 21–22. 21. The plane through P0(2, 4, 5) perpendicular to...

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

Q: Find a formula for the distance from the point P(x, y, z) to the a. x-axis. b. y-axis c. z-axi...

A: The formula for distance between two points (x, y, z) and (a, b, c) is

Q: In a psychology experiment, a person could memorize x words in f(x) = 3x2 − x seconds (for 0 ≤ x ≤...

A: a person could memorize x words in f(x) seconds where

Q: What is a cycloid? What are typical parametric equations for cycloids? What physical properties acco...

A: Click to see the answer

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: Find the particular solution of the differential equation

A: The given D.E. is the first order separable O.D.E.Rearrange the given D.E.

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

A: Click to see the answer

Q: Find the coordinates of the centroid of the curve x = cos t, y = t + sin t, 0<=t <= pai.

A: Click to see the answer

Q: Show that the point P(3, 1, 2) is equidistant from the points A(2, -1, 3) and B(4, 3, 1).

A: Let the distance between P(3, 1, 2) and A(2, -1, 3) be d1 and the distance between P(3, 1, 2) and B(...

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: 1.Given vectors are

Q: Find the limit

A: Plug x=2 for the limit.

Q: A force F = 2i + j - 3k is applied to a spacecraft with velocity vector v = 3i - j . Express F as a ...

A: We have given the force F = 2i + j - 3k with velocity vector v = 3i – j.

Q: Show that the diagonals of a rhombus (parallelogram with sides of equal length) are perpendicular.

A: Show that the diagonals of a rhombus (parallelogram with sides of equal length) are perpendicular

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

A: Click to see the answer

Q: Find the points in which the line x = 1 + 2t, y =-1 - t, z = 3t meets the coordinate planes. Describ...

A: The given lines are,

Q: What is a Maclaurin series?

A: The Maclaurin series of f is the Taylor series generated by,

Q: The approximation ex = 1 + x + (x2/2) is used when x is small. Use the Remainder Estimation Theorem ...

A: The given approximation is a second order Maclaurin polynomial for ex. We get an upper bound for R3...

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 dimensions of the rectangle of largest area that can be inscribed in the ellipse x2 + 4y2 =...

A: Click to see the answer

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

A: (1)

Q: Exercise 5: Some weird integral problems. Solve at least three; the remaining three are challenge on...

A: Solve the given integration

Q: a. Use Taylor’s formula with n = 2 to find the quadratic approximation of ƒ(x) = (1 + x)^k at x = 0 ...

A: Given:Use Taylor’s formula with n = 2 to find the quadratic approximation of ƒ(x) = (1 + x)^k at x =...

Q: Find the area enclosed by the ellipse x = a cos t, y = b sin t, 0<= t<= 2pai.

A: Given,