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Q: give the eccentricities of conic sections with one focus at the origin along with the directrix corr...

A: Problem 1:Recall the following fact.

Q: In the function: f(x)= 6/((x^2)-16) Where is the function concave up and down in interval notation...

A: Given,

Q: Find the centroid of the region that is bounded below by the x-axis and above by the ellipse (x2/9) ...

A: As shown in the figure the ellipse is bounded below by x-axis.It is clear from the symmetry that the...

Q: Find parametric equations for the semicircle x2 + y2 = a2, y> 0, using as parameter the slope t =...

A: Click to see the answer

Q: Find an equation for the parabola with focus (4, 0) and directrix x = 3. Sketch the parabola togethe...

A: Given that the focus of the parabola is (4, 0) and its directrix is x = 3. Observe that the focus li...

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: dy/dx (y=x^2(4x+1)^3)

A: To find dy/dx we differenciate both sides with respect to x.On the right side use the Product rule.(...

Q: Find the average rate of change of the given function between the following pairs of x-values. f(x)...

A: Given:

Q: (2x + 4y) + (2x − 2y)y′ = 0

A: Consider the provided differential equation.

Q: What is an improper integral of Type I? Type II? How are the values of various types of improper int...

A: The improper integrals may be defined based on the continuity of the integrand inside them within th...

Q: n Exercises 17–23, find the eccentricity of the hyperbola. Then find and graph the hyperbola’s foci ...

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Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 <=t<= 2pai closest to the point (3/4, ...

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Q: Use the given transformation to evaluate the integral. lr a?dA, where R is the region bounded by the...

A: Given,

Q: I need to compute each limit. The limit is ... lim x -> 0 4(x+1)2+3(x+1)-7 ————— x

A: Click to see the answer

Q: Sketch the circles in Exercises 53–56. Give polar coordinates for their centers and identify their r...

A: Note: We’ll answer the 53rd question since we answer only one question at a time. Please submit a ne...

Q: Find an equation for the set of points equidistant from the y-axis and the plane z = 6.

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

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: Solve the differential equation listed below:

A: Separate the variables.

Q: y′ = e2x + y − 1

A: Given,

Q: find the Taylor series at x = 0 of the functions in Exercises 1–5. 1. e^-5x 2. sin ( paix/ 2) 3. ln ...

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

Q: Show that the curves 2x2 + 3y2 = 5 and y2 = x3 are orthogonal.

A: To show that the two curves are orthogonal.

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

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Q: Write inequalities to describe the sets in Exercises 45–46. 45. The half-space consisting of the poi...

A: Since we only answer up to 1 question, we’ll answer the first question. Please resubmit the question...

Q: I need help evaluating a derivative of a function at the point (pi/2,18pi)

A: We have given

Q: Solve the differential equations in Exercises 1–4. 1. x dy /dx + y = ex, x> 0 2. xy′ + 3y = sin x...

A: Consider the provided differential equation,

Q: Find the centroid of the region in the plane enclosed by the curves y = +-(1 - x2)^(-1/2) and the li...

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

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Q: Exercises 1–4 give equations of parabolas. Find each parabola’s focus and directrix. Then sketch the...

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If y...

Q: Find the point equidistant from the points (0, 0, 0), (0, 4, 0), (3, 0, 0), and (2, 2, -3).

A: Find the point equidistant from the points (0, 0, 0), (0, 4, 0), (3, 0, 0), and (2, 2, -3).

Q: Marcos traveled for 2 hours and 17 minutes on Interstate 17 as he drove (without stopping) a distanc...

A: Given:Marcos travelled a distance of 155 miles in 2 hours and 17 minutes.

Q: Show that a unit vector in the plane can be expressed as u = (cos u)i + (sin u)j, obtained by rotati...

A: To show that a unit vector can be expressed as u = (cos u) i + (sin u) j.

Q: Write inequalities to describe the sets in Exercises 45–46. 45. The slab bounded by the planes z = 0...

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

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: In Exercises 1–8, find the eccentricity of the ellipse. Then find and graph the ellipse’s foci and d...

A: Click to see the answer

Q: A wheel of radius a rolls along a horizontal straight line without slipping. Find parametric equatio...

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Q: Find the limit. lim In(x² – 1)

A: Given,

Q: A bird flies from its nest 5 km in the direction 60° north of east, where it stops to rest on a tree...

A: A bird flies from its nest 5 km in the direction 60° north of east, where it stops to rest on a tree...

Q: What consequence does the lack of uniqueness of polar coordi-nates have for graphing? Give an exampl...

A: Click to see the answer

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: If possible, solve for 3A + 2B

A: Using basic operation of multiplication and addition of matrices to solve the given expression.First...

Q: describe the given set with a single equation or with a pair of equations. The plane through the poi...

A: Describe the given set with a single equation or with a pair of equations. The plane through the poi...

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: In Exercises 25–26, express each vector as a product of its length and direction. 25. 5k 26. 3/5i+4/...

A: We’ll answer the 25th question since we answer only one question at a time. Please submit a new ques...

Q: I need help finding an equation of the tangent line to the function y= cos(3x) with the point ((pi)/...

A: Given:

Q: Find all points that simultaneously lie 3 units from each of the points (2, 0, 0), (0, 2, 0), and (0...

A: Let such a point is (x,y,z)

Q: If C is the curve given by r (t) = (1+2 sint)i+ (1+ 2 sin? t)j+ (1+1 sin' t) k, 0<t< and F is the ra...

A: Given:

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,