If ry3 + y2 + 2r2-2 + 6y (i) determine dy, where r is an independent variable and y is a function of r. Simplify as much as possible. (ii) Find the equation of the tangent line at -1 dr

Q: Use any method to determine if the series converges or diverges. Give reasons for your answer.

A: Refer to the question.Here we have to find the convergence of the series,

Q: Hello, How is tan^-1 (tan (6pi/7)=-pi/7 possible? I don't know how it should be a negative or to use...

A: First consider:

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A: You have asked two unreleated questions in the same post. Further your first question has multiple s...

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A: f will be increasing if f'(x)>0. From the graph of f'(x) we see f'(x)>0 when x>3 [because a...

Q: Approximate the area of the shaded region using the Trapezoidal Rule and Simpson's Rule with n = 4. ...

A: Given information:The value of n is 4. 

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is inf...

A: We first have to factor the numerator and the denominator. 

Q: 2 -4 0 such that f(x)-4 0, make a conjecture about the value of 8 that satisfies the preceding ineq...

A: For part a, bAccording to epsilon delta limit.Let f(x) be the function defined on an open interval a...

Q: y′=−2ex −2x2 +3x+6 y(0)=5 Solve the initial value problem above. Do not include "y=" in your answer.

A: Given that  y′ = -2ex -2x2 +3x +6; y(0) = 5.That is dy/dx = -2ex -2x2 +3x +6.dy =(  -2ex -2x2 +3x +6...

Q: Which of the following is the power series representation for g(x)? +8 OA. B. k 8 1 k 0 k 0 8k O C. ...

A: Note that the function g(x) is not provided (here option (c) can also be a power series). So, we are...

Q: The number of miligrams x of a medication in the bloodstream t hours after a dose is taken can be mo...

A: we are given a function  

Q: Find the position and velocity of an object moving along a straight line with the given acceleration...

A: Integrate the acceleration and find the velocity.

Q: find the exact length of the curve of the equation below, show all work y = ln(sec(x)), with a range...

A: First, we find the dy/dx

Q: What's the domain of x-1 / (1 - e^(x - 3))

A: Since this function is a rational function, the denominator can't be equal to 0. 

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by th...

A: (d) First draw the graph of y = x + 6 and y = x2.Find the intersection points as,

Q: Question: Find the area of the region bounded by y y0, x1, x-4

A: The area of region bounded by the curve y=(x^2+x-1)/((x)^1/2), x=1,x=4,y=0.

Q: Find the derivative of the inverse function  f(x) = x/x+2

A:

Q: How can I get the result? Which is the result?

A: We have to find limits.Question is given below:

Q: 3x4 y‴+9x4 =5xy′+5x5 y″+9lnx   Determine the order of the differential equation shown above.

A: The given differential equation is,

Q: dy If y 22 x, then dx 9.7 1. O 22 0. O 5. N O O O OO

A: The given equation is y=22+x.

Q: Evaluate the following integral.

A: The given integral is,

Q: This is #1

A: Part (a)Consider an object moving along a line with the velocity and initial position.

Q: p(q)=2q2-4q+5; q=2 (a) Find the derivative, by using the definition. (b) Find the instantaneous rate...

A: Part (a)The derivative of p(q) at any point q, by using the definition, will be given by the express...

Q: a. Write the equation of the line that represents the linear approximation to the following function...

A: We have to find f'(x) first. 

Q: Part d and e

A: (D) When the enclosed region revolve about x=2 line then the radius is on the line joining (2,0) and...

Q: A​ hot-air balloon is 190 ftabove the ground when a motorcycle​ (traveling in a straight line on a h...

A: Let x be the horizontal distance from balloon to motorcycle, y be the vertical distance from the bal...

Q: Suppose f is differentiable on an interval containing a, b, and let P(a,f(a)) and Q(b,f(b)) be disti...

A: Given information:Suppose f is differentiable on an interval containing a, b, and let P(a,f(a)) and ...

Q: Please show as much steps as possible as I am doing my best to fully understand how to solve these t...

A: Given function is, 

Q: The graphs of y=1.1x and y=x have two points of intersection, while the graphs of y=2^x and y=x have...

A: Here, we are given that for a real number 1< p < 2 , the graphs of y=px and y=x have exactly o...

Q: dy Ify드a2-4x-의. then. dx x2 2x-2) 2-4x-5 einz2-4x-5)- In(z+2)]. x2-4x-5 x2 x2-4x-5 x 2 x 2 2-4x-5 x2...

A: Consider the given equation:

Q: solve 6^(x+3) = 2 for x

A: We take ln on both sides. 

Q: 2ex/2 dx = 0 1 (e-1) 1 (e-1) e 1 2(e-) 4(e

A: Given:The integral is 

Q: please explain how to solve this problem

A: Consider x be the number of times the price is reduced by $0.05.

Q: Help w/ #6

A: The curve is given by ti+t2j+t3k.The formula to calculate the curvature of the curve is given by,

Q: Use the Divergence Theorem to compute the net outward flux of the vector field F=<x2 , -y2, z2&gt...

A: The vector field is given as

Q: 1000 Find the marginal cost when q = 10. 9 The average coste for producing q units of a product is g...

A: The average cost c is given by ,

Q: SImplify   (h3-4h)/(h3-2h2)

A: Simplify the given expression as follows.

Q: I got up to:   60-62t, then started doing  30 + the integral from t to 0 but I don’t know if I’m doi...

A: To find velocity we have to integrate a(t)= -62Answer: Velocity: v(t)=-62t+60

Q: 1) If an odd function h(x) has a local maximum value at x c, can anything be said about h at the val...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: A drag racer accelerates at a(t) = 84 ft/s^2. Assum v(0) and s(0) = 0.

A: Since we are entitled to answer up to 3 sub-parts, we’ll answer the first 3 as you have not mentione...

Q: Calculus Question

A: Let's call the given integral as I. Further let's make the substitution: x2 + 1 = zHence, 2xdx = dzP...

Q: If l0g x=0.35 and fog6N0.5, evaluate the fo llowig expression.

A: Here, we use the above log rules.

Q: find the volume aquired by taking by region bound by  y=x^2 and  y=x^4 and rotating it around x=-1

A: To calculate the volume bounded by the curve y=x2 and y=x4 which is rotating about the line x=-1. No...

Q: 3x2-3 and y(0) = 8, then y(1) = If dx 4. 12. 0. 8 6.

A: As a first step, let\'s rearrange the term. Please see the white board. 

Q: If given the differential equation y''-4y'+4y=et, is there a way to solve it for possible solutions?...

A: we are given a differential equation as  

Q: Sketch the region of integration and evaluate the following integrals. Please refer to attached imag...

A:

Q: Logarithmic Differentiation - See attachment

A: Find the derivative of the given function.

Q: 7n 5-4n For the following answer blanks, decide whether the given sequence or series is convergent o...

A: (a)we are given a series as 

Q: How can I get the result? Which is the result?

A: we are given a function as 

Q: During the first 4 months of employment, the monthly sales S (in thousands of dollars) for a new sal...

A: During the first 4 months of employment, the monthly sales S (in thousands of dollars) for a new sal...

Q: What is the velocity at time t for a car that begins accelerating at a rate of 4 feet per second squ...

A: To determine the velocity from the given conditions