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What is the limit?

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Calculus

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Q: Find the derivative of the following function and evaluate the derivative at the given value of x. f...

A: The given function is,

Q: Let u = 2i + j, v = i + j, and w = i - j. Find scalars a and b such that u = av +bw.

A: Given u = 2i + j, v = i + j, and w = i - j.Plug them in the equation u = av +bw.

Q: Given nonzero vectors u, v, and w, use dot product and cross product notation, as appropriate, to de...

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Q: Can someone show me how to get to the answer in the problem?

A: Given integral

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

Q: Show that the vector v = ai + bj is parallel to the line bx - ay = c by establishing that the slope ...

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A: sphere of radius 5 centered at the origin is given by:

Q: Solve the inequality. Write your answer in interval notation. |5x - 4| ≤ 7

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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: find a parametrization for the curve. 1. the left half of the parabola y = x2 + 2x 2. the ray (hal...

A: Part 1;Given curve is

Q: find the component form of the vector. The vector 5 units long in the direction opposite to the dire...

A: Given vector (3/5)i+(4/5)j is unit vecor as its magnitude is 1

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Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections in Ex...

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

Q: Find the volume V of the described solid S. The base of S is the region enclosed by the parabola y =...

A: Click to see the answer

Q: please solve and show your work

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

Q: What points in the xy-plane satisfy the equations and inequalities in Exercises 11–12? Draw a figure...

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

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: Find the distance between the point (1,1) and (3,9) along the curve y=x2

A: Given:The points (1,1) and (3,9) along the curve y=x2To find the distance we need use calculus as th...

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

A: To describe the geometric curve satisfied by the equation.

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 lengths of the curves in Exercises 25–27. 25. x = cos t, y = t + sin t, 0 <=t<= pai 2...

A: The given curve is

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

A: Given,

Q: 12. Find the domain of the function: -(20/13)x + (30/13) 16. Find the domain of the function: sqrt(u...

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

Q: In the function: f(x)= (7x+B)/(4x+b) , with 7b>4B When is the function increasing and when is th...

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A: (a) Obtain the Riemann sum for the given integral using right endpoints and n = 3 as follows.

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A: Given, vertices of the triangle are

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A: Show that a projectile attains three-quarters of its maximum height in half the time it takes to rea...

Q: Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x = 2s + 2, y = s + 3,...

A: Given lines are x = t, y = -t + 2, z = t + 1, and x = 2s + 2, y = s + 3, z = 5s + 6Set the x and y ...

Q: Besides geometric series, what other convergent and divergent series do you know?

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Q: Find the acute angle between the planes x = 7 and x + y + sqrt(2)z =-3.

A: We know that cosine of angle between plane a1x+b1y+c1z=d1 and a2x+b2y+c2z=d2 is given by

Q: 71. The square roots, cube roots, and fourth roots of + are shown in the figure from left to right, ...

A: To determine the nth root of 1 using the pattern.

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

A: Given,

Q: What is the rule when dividing rational expressions

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Q: Find an equation for the set of points equidistant from the a. xy-plane and yz-plane. b. x-axis and ...

A: a) Let (x,y,z) be such point that xy-plane and yz-plane are equidistant from it.Distance of (x,y,z) ...

Q: Exercises 49–50 give equations for ellipses and tell how many units up or down and to the right or l...

A: Note: We’ll answer the 49th question since we answer only one question at a time. Please submit a ne...

Q: What angle does the line of intersection of the planes 2x + y - z = 0 and x + y + 2z = 0 make with t...

A: Given:The planes 2x + y - z = 0 and x + y + 2z = 0

Q: Find the centroid of the region enclosed by the x-axis and the cycloid arch x = a(t - sin t), y = a(...

A: Given data:

Q: In Exercises 25–26, express each vector as a product of its length and direction. 25. 2i + j - 2k 26...

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

Q: Find the distance from the a. x-axis to the plane z = 3. b. origin to the plane 2 = z - x. c. point ...

A: a) z=3 is parallel to x axis. It is 3 units above x axis. ( Refer to the diagram)Answer: 3

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

A: Given functions are

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: 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: Find parametrizations for the lines in which the planes in Exercises 61–64 intersect. 61. x + y + z ...

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A: Given:

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.