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

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

Q: obtain a slope field and add to it graphs of the solution curves passing through the given points. y...

A: Click to see the answer

Q: Determine if the following radical expression is a real number?. √-25

A: Given the radial expression √-25

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

A: 1)Given,e = 1, y = 2 Equation of conic with eccentricity e and directrix y=k corresponding to focus ...

Q: How many terms of the Taylor series for ln (1 + x) should you add to be sure of calculating ln (1.1)...

A: The Taylor series for ln(1+x) can be written as:

Q: What is a Maclaurin series?

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

Q: The given equation is either linear or equivalent to a linear equation. Solve the equation. (If ther...

A: Given,

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 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: 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: Let y be the percent increase in annual US national production during a year when the unemployment r...

A: a) If we plug u=0 in y=3.5-2u then we get y=3.5 .u=0 means no change in the unemployment rate.So 3.5...

Q: How do you find the length of a smooth parametrized curve x = ƒ(t), y = g(t), a<= t<=b? What d...

A: Given data:

Q: Replace the Cartesian equations in Exercises 56–61 with equivalent polar equations. 56. x - y = 3 57...

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

Q: The region in the first quadrant enclosed by the coordinate axes, the curve y = ex, and the line x =...

A: To determine the volume of the solid of revolution about the y-axis.

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

A: Given that,

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

A: Let any such point is given by (x,y,z)(x,y,z) is z units away from the xy plane.

Q: What is an orthogonal trajectory of a family of curves? Describe how one is found for a given family...

A: There are some conditions for the orthogonal trajectories.

Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the re...

A: Sketch the integrant as shown below.

Q: Use a graphing utility to graph the function and estimate the limit. Use a table to reinforce your c...

A: The graph has been plotted using the graphing utility as asked in the question.

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: 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: A tank contains 100 gal of fresh water. A solution containing 1 lb/ gal of soluble lawn fertilizer r...

A: Calculation:

Q: Find the angle between the radius vector to the curve r = 2a sin 3u and its tangent when u = pai/6.

A: Click to see the answer

Q: A reservoir shaped like a right-circular cone, point down, 20 ft across the top and 8 ft deep, is fu...

A: Given: A reservoir shaped like a right-circular cone, point down, 20 ft across the top and 8 ft deep...

Q: Find all polar coordinates of the origin.

A: We know that when we convert cartesian coordinates into polar coordinates, then we use the relation

Q: Solve the exponential growth/ decay initial value problem for y as a function of t by thinking of th...

A: Given,

Q: Solve the following initial value problem for u as a function of t: du/dt+k/ m u = 0 (k and m positi...

A: Plug du/dt = u' to make it first-order linear equation.

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

A: Click to see the answer

Q: A brief calculation shows that if 0<=x<= 1, then the second de-rivative of ƒ(x) = sqrt(1 + x4)...

A: The Given information is,

Q: An executive conference room of a corporation contains 4500 ft3 of air initially free of car-bon mon...

A: Let y(t) be the amount of carbon monoxide in that conference room at time t.

Q: What is a parabola? What are the Cartesian equations for parabo-las whose vertices lie at the origin...

A: Explanation:

Q: Use this formula to find the instantaneous rate of change of the function at the given x-value.f(x) ...

A: Given function is

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...

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

A: Click to see the answer

Q: Find the point on the parabola x = t, y = t2, -infinity<=t <=infinity, closest to the point (2...

A: Consider the required point as (x,y)Consider the formula of distance between the two points.

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: In the function: f(x)= (3x^2)ln(x) , x>0 When is the function concave up and concave down in int...

A: For concavity we need second derivative.

Q: Consider the region R in the ry-plane that is described by the intersection of the four lines: 6x – ...

A: First of all, use the transformation given.

Q: (2x + 3) + (2y − 2)y′ = 0

A: Given,

Q: Find equations for the sphere whose center and radius is given in center(0,-7,0) radius 7

A: General equation of sphere is given by:

Q: For the function f,Construct and simplify the difference quotient f(x+h)-f(x)/h

A: Given:

Q: Find the distance from the point (4, 3, 0) to the a. x-axis b. y-axis c. z-axis

A: To determine the distance of the point from,Part (a) x-axisPart (b) y-axisPart (c) z-axis

Q: a ball is thrown straight upwards from a tower (40 feet high) so that its position, s in feet, at ti...

A: Click to see the answer

Q: Estimate the error if P 3(x) = x - (x^3/6) is used to estimate the value of sin x at x = 0.1.

A: Given: