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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 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 Exercises 1–3, a. Identify the equilibrium values. Which are stable and which are unstable? b. Co...

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,...

Q: For approximately what values of x can you replace sin x by x - (x3/6) with an error of magnitude no...

A: The Taylor series for sin(x) can be written as:

Q: Let f(x) = {4x-5, if x <= 7 -3x + b, if x > 7 If ?(?)f(x) is a function w...

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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: 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: Find the vertex, focus, and directrix of the parabola x2 - 6x - 12y + 9 = 0.

A: Write the given parabola in standard form by completing square

Q: 4x² + 5 -dx 3

A: Given, integral is

Q: Find the volume swept out by revolving the region bounded by the x-axis and the graph of x = 2t, y =...

A: Given that x = 2t and y = t(2–t). Obtain the interval of integration as follows.

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

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

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Q: What is a hyperbola? What are the Cartesian equations for hy-perbolas centered at the origin with fo...

A: Problem 1:Recall the following fact.

Q: #1

A: Given differential equation and its solution is

Q: Express as a single logarithm and if possible simplify

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

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Q: What is an autonomous system of differential equations? What is a solution to such a system? What is...

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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: 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: #13

A: Given,

Q: In the function: f(x)= (7x+B)/(4x+b) , with 7b>4B At which x-coordinates are there points of inf...

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Q: a. Find the length of one arch of the cycloid x = a(t - sin t), y = a(1 - cos t). b. Find the area o...

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Q: How can you sometimes use power series to estimate the values of nonelementary definite integrals? T...

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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: 3. Write the function defined by fx) = -2x2- 12x in vertex form and identify the vertex of the parab...

A: Given,

Q: If cos x is replaced by 1 - (x2/2) and |x |<0.5, what estimate can be made of the error? Does 1 -...

A: We’ll answer the second question first. Notice the question have used first two digits of Maclaurin ...

Q: How can you estimate the error involved in approximating the sum of an alternating series with one o...

A: The alternating series test:

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: What tests are available for determining the convergence and divergence of improper integrals that c...

A: The tests available for determining the convergence and divergence of improper integrals that cannot...

Q: Find the areas of the surfaces generated by revolving the curves in Exercises 31–34 about the indica...

A: We’ll answer the 31th question since we answer only one question at a time. Please submit a new ques...

Q: Determine whether the sequences are increasing, decreasing, or not monotonic. If increasing, enter 1...

A: Find the sequence increasing, or decreasing or not monotonic.

Q: Find all real zeros of the function. g(x)=5(x2-36)(x-7)(x+7)2

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

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Q: In the function: f(x)= (3x^2)ln(x) , x>0 What are the critical numbers of the function?

A: Given function is

Q: The ellipse (x2/9) + (y2/25) = 1 is shifted 3 units to the left and 2 units down to generate the ell...

A: Given,

Q: Find Power Series representations of the following functions (a) f(x) = 3x12 – æ5 f(x) = In(x +1) (b...

A: (a)Given

Q: How do you reindex a series? Why might you want to do this?

A: Any series can be reindexed without changing its convergence.

Q: Use Simpson’s Rule to approximate the av-erage value of the temperature function ƒ(x) = 37 sin (2pai...

A: Given information:

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

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Q: Hi, I have some homework for my calculus class that I can't figure out. I worked it out and got it w...

A: Given,

Q: •5 6- Let f(x)dx = 10, f(x)dx = 9, f f(x)dx = 2. Find f(x)dx and (10f(x) – 9)dx =

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

A: To determine the equation of a line passing through (1, 3,-1) parallel to,Part (a) x-axisPart (b) y-...

Q: The temperature at which water starts to boil (its boiling point) is linearly related to the altit...

A: Let 1000x ( x times 1000) feet above sea level you need to be in order to have a boiling point of 1...

Q: I need to compute each limit. The limit is ... lim x -> 1 x - 1 ————— 2 - the square root of x +...

A: According to the given information it is required to calculate the limit of the function.

Q: The Cinema Center consists of four theaters: Cinemas I, II, III, and IV. The admission price for one...

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Q: What happens if you add a finite number of terms to a convergent series? A divergent series? What ha...

A: As there are multiple parts to the question, we will address the par related to divergent series fir...

Q: a. Graph the hyperbolic spiral ru = 1. What appears to happen to c as the spiral winds in around the...

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