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Q: Use the identity sin^2 x = (1 - cos 2x)/2 to obtain the Maclaurin series for sin^2 x. Then different...

A: It is given that

Q: y′=2x/(1+2y),y(2)=0

A: Click to see the answer

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: 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: Express as a single logarithm and if possible simplify

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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: 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: What is a Maclaurin series?

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

Q: A company produces wooden tables. The company has fixed costs of $2900, and it costs an additional $...

A: Recall that: Profit = Revenue – Expense

Q: Use the Taylor series for 1/ (1 - x2) to obtain a series for 2x/ (1 - x2)2.

A: Click to see the answer

Q: What is the age of a sample of charcoal in which 90% of the carbon-14 originally present has decayed...

A: Consider half-life for charcoal sample.

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

A: We have given

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

A: Given information:

Q: Use the equation ƒ(x) = ƒ(a) + ƒ′(a)(x - a) + ƒ′′(c2) /2 (x - a)2 to establish the following test. L...

A: For the given function to determine its behaviour at a critical point x=a, use second derivative tes...

Q: if you have a parametric equation grapher, graph the equations over the given intervals x = 2 cos t ...

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Q: Let f(t) be the piecewise linear function with domain 0 <t < 8 shown in the graph below (which is de...

A: By observing the graph, Write the values of the function A(x) at respective x.

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: A phone company charges $16.95 a month and 12 cents for every minute above 120 minutes. Write an exp...

A: A phone company charges $16.95 a month and 12 cents for every minute above 120 minutes. Write an ex...

Q: solve the following equation for X. 3*e^2x+7*e^x+2=0

A: Given,

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

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

A: Given,

Q: Find the length of the curve y = ln (sin x), pai/6<=x<=pai/2.

A: The given curve is,

Q: How would you compare the relative merits of Simpson’s Rule and the Trapezoidal Rule.

A: Compare the relative merits of Simpson’s rule and the Trapezoidal rule as given below in the Table

Q: Find, to two decimal places, the x-coordinate of the centroid of the region in the first quadrant bo...

A: Given the x-coordinate of the centroid of the region in the first quadrant bounded by the x-axis, th...

Q: Find the limit. (If an answer does not exist, enter DNE.) lim (x + Ax)2 - 9(x + Ax) + 3 - (x2 – 9x +...

A: Given:

Q: Find the volume of the solid generated by re-volving the region in the first quadrant bounded by the...

A: We need to find the volume of the solid generated by revolving the region in the first quadrant boun...

Q: find an equation for the line tangent to the curve at the point defined by the given value of t. Als...

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

A: Given:

Q: How can you sometimes find the area bounded by a parametrized curve and one of the coordinate axes?

A: Let the equation of parametrized curve be

Q: Find parametric equations and a parameter interval for the motion of a particle that starts at (a, 0...

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Q: What are polar coordinates? What equations relate polar coordi-nates to Cartesian coordinates? Why m...

A: Consider an origin as O and an initial ray from the origin. The positive x-axis is usually considere...

Q: dy/dx of y=e^3x+1

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Q: a. Use Taylor’s formula with n = 2 to find the quadratic approximation of ƒ(x) = (1 + x)^k at x = 0 ...

A: Given:Use Taylor’s formula with n = 2 to find the quadratic approximation of ƒ(x) = (1 + x)^k at x =...

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: What values of p have the following property: The area of the region between the curve y = x^-p, 1&l...

A: Given information:

Q: (y/x+6x)+(ln x−2)y′=0,x>0

A: Consider the given differential equation.

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: The region between the curve y = 1/(2sqrt(x)) and the x-axis from x = 1/4 to x = 4 is revolved about...

A: (a) The given curve is

Q: Find the value of c so that ƒ(x) = csqrt(x)(1 - x) is a probability density function for the random ...

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

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: Obtain the Taylor series for 1/(1 + x)2 from the series for -1/(1 + x).

A: Recall the following fact.

Q: What is the formula for the slope dy/dx of a parametrized curve x = ƒ(t), y = g(t)? When does the fo...

A: Given parametric curves are

Q: Suppose that q = f(p) is the demand curve for a product, where p is the selling price in dollars and...

A: Given:

Q: (3x + 4x + 5) dx (a) Find the Riemann sum for this integral using right endpoints and n = 3. 454 (b)...

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

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: The digestion time in hours of a fixed amount of food is exponentially distributed with a mean of 1 ...

A: The exponential density function is,

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

A: Given,

Q: I need to compute each limit. I have attached the problem as a photo.

A: Given:

Q: The concentration of an antihista-mine in the bloodstream of a healthy adult is modeled by C = 12.5 ...

A: 6 hour period means from t=0 to t=6That is from start of the medication to 6 hours after medication...