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CalculusQ&A LibraryExercise. The position vector for a particle is described by the vector-valued function: sin(at) r(t) = cos(at), for t > 0. Find (positive) a so the curve uses arc length as a parameter. Exercise. Let C be a curve drawn by: r(t) = (sin(t) – 1, 2 sin(t) + 2, –2 sin(t)) Find the length of the curve drawn by r ast runs from -T/2 to T/2: lengthStart your trial now! First week only $4.99!*arrow_forward*

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Q: find the derivative (dy/dx) of the given function: 1. y= e^X sin X 2. y= (cos x)^9 3. 1/ ln(X) 4. ...

A: Given,

Q: Find the area of the parallelogram with vertices K(3, 2, 1), L(3, 5, 3), M(5, 10, 3), and N(5, 7, 1)...

A: To find the area of the given parallelogram, use the vector method which is described as.We know tha...

Q: a. Show that every vertical line in the xy-plane has a polar equation of the form r = a sec u. b. Fi...

A: Calculation:

Q: Find the volume of the solid formed by revolving the re-gion bounded by the graphs of y = sin x + se...

A: The given graph of the functions are

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: 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: sin(2x) dx+cos(3y) dy=0,y(π/2)=π/3

A: Given:

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: 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: Let ƒ(x) = c/(1 + x2) . Find the value of c so that ƒ is a probability c density function. If ƒ is a...

A: Write the given expression and simplify it using the definition of probability density function.

Q: Consider the region bounded by the graphs of y = sqrt(x tan-1 x) and y = 0 for 0 <=x<= 1. Find...

A: Given,

Q: Find the area of the region in the first quadrant that is enclosed by the coordinate axes and the cu...

A: Given: Find the area of the region in the first quadrant that is enclosed by the coordinate axes and...

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

A: (a)Given

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: 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: 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: The college must build a wheelchair ramp to provide wheelchair access to a building. Federal buildin...

A: We model the equation to suit the criteria given. Question reads that for every 12 inch horizontal d...

Q: ư (yũ + Vũ) du =

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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: 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: The estimate sqrt(1 + x) = 1 + (x/2) is used when x is small. Estimate the error when | x|< 0.01.

A: Taylor inequality state that, M is a positive real number such that

Q: The college must build a wheelchair ramp to provide wheelchair access to a building. Federal buildin...

A: Consider the linear function defined below that models the height, H of ramp above the ground as a f...

Q: Suppose n is an integer. So Show that for n+0, ſ x cos(nx)dx = { п n is even (a) 2 п is odd n2

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Q: What integral equation is equivalent to the initial value problem y′ = ƒ(x), y(x0) = y0?

A: Write y'= dy/dxThen separate the variables.

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

A: Explanation:

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

A: Calculation:

Q: What are the Taylor series for 1/(1 - x), 1/(1 + x), ex, sin x, cos x, ln (1 + x), and tan-1 x? How ...

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Q: a. If (ln x)/x = (ln 2)/2, must x = 2? b. If (ln x)/x = -2 ln 2, must x = 1/2? Give reasons for your...

A: Given:If (ln x)/x = (ln 2)/2, must x = 2? ……... (1)If (ln x)/x = -2 ln 2, must x = 1/2? …….. (2)

Q: What is a monotonic sequence? Under what circumstances does such a sequence have a limit? Give examp...

A: The monotonic sequence theorem:

Q: If you use the approximation ln 2 ≈ 0.70 (in place of 0.69314 c), you can derive a rule of thumb tha...

A: Given a rule of thumb that says, “To estimate how many years it will take an amount of money to doub...

Q: Find the values of the variables. 1 1 x 4 1 13 3 3 z %3D 4 2 х IL || ||

A: Given:

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

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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: In the function: f(x)= (7x+B)/(4x+b) , with 7b>4B What are the critical numbers of the function?

A: Given:

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: 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: I just need #30

A: Given:

Q: consider the equation f(x) = 2x2 - x Find the net change between x = 3 and x = 6

A: Given equation:

Q: Give some typical parametrizations for lines, circles, parabolas, ellipses, and hyperbolas. How migh...

A: First of all, consider the cartesian form of the equation for the line.Then, consider the parametriz...

Q: Graph ƒ(x) = tan-1 x + tan-1(1/x) for -5<=x<=5. Then use calculus to explain what you see. How...

A: Simplify the function first in order to make its graph look easier, which can be done using trigonom...

Q: Evaluate the limit, if it exists:

A: LCM of (x+h)^2 and x^2 is x^2*(x+h)^2.Simplify the numerator using LCD.

Q: A tank initially contains 120 L of pure water. A mixture containing a concentration of γ g/L of salt...

A: A tank initially contains 120 L of pure water. A mixture containing a concentration of γ g/L of salt...

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Q: I need to compute each limit. The limit is ... lim x -> -3 x2 + x - 6 ————— x3 + 27

A: Given,

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

A: Given: