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A: Given,

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A: Given information:

Q: Find the length of the curve y = ln(e^x - 1) - ln(e^x + 1), ln 2<=x<= ln 3.

A: Given:

Q: (2x + 4y) + (2x − 2y)y′ = 0

A: Consider the provided differential equation.

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A: Click to see the answer

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A: Given,

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A: First of all, consider the method to find weather the infinite series is diverging or converging.

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A: Given,

Q: Find the lengths of the curves in Exercises 4-8. If you have graphing software, you may want to grap...

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

Q: Use the definitions of cosh x and sinh x to show that cosh2 x - sinh2x = 1.

A: To show that cosh2x - sinh2x =1.

Q: 1 +(x/y − sin y)y′ = 0

A: 1 +(x/y − sin y)y′ = 01 +(x/y − sin y)dy/dx = 0dx +(x/y − sin y)dy = 0Here M(x,y) = 1 and N(x,y) = (...

Q: consider the product of 3 functions w= f x g x h. Find an expression for the derivative of the produ...

A: Given functions are f, g , hTheir derivatives are given by f ' , g ' , h '

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A: Given information:

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A: Find the moment about the x-axis of a wire of constant density that lies along the curve y = x3 from...

Q: How do you define and calculate the area of the surface swept out by revolving the graph of a smooth...

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Q: Consider a region bounded by the graphs of y = x4 and y = x5. Show that the center of mass lies outs...

A: It is given that the density of the plate is and the region bounded by the graphs of y = x4 and y =...

Q: Find the volume of the solid generated by revolving the region in the first quadrant bounded by the ...

A: Recall the fact.

Q: What is the exact value for cos(cos-1(1))

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Q: solve the differential equation. 1.e-x dy + (e-xy - 4x) dx = 0 2. (x + 3y2) dy + y dx = 0 (Hint: d(x...

A: Consider the provided differential equation,

Q: The infinite region bounded by the coordinate axes and the curve y = -ln x in the first quadrant is ...

A: Express the integral as below.

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: In Exercises 25–27, find the derivative of y with respect to the appro-priate variable. 25. y = sinh...

A: Hey since there are multiple questions the first question is answered and repost the question if any...

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) lim h→0 (5 + h)−1 ...

A: To evaluate the limit

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A: Given:

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A: It is given that the mountain climber is about to haul up a 50-m length of hanging rope.Find the fun...

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A: Click to see the answer

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A: Consider the provided autonomous differential equation,

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A: Click to see the answer

Q: The business manager of a 90 unit apartment building is trying to determine the rent to be charged. ...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: Use the Euler method with dx = 0.5 to estimate y(5) if y′ = y2/sqrt(x) and y(1) =-1. What is the exa...

A: Consider the formula used in Euler’s method.Also summarize the given data in the question.

Q: In the function: f(x)= (3x^2)ln(x) , x>0 Where is the function increasing and decreasing in inte...

A: Click to see the answer

Q: consider the equation f(x) =5x2 find the average rate of change between x=3 and x=3+x

A: Given: the equation f(x) =5x2 and find the average rate of change between x =3 and x =3+ x

Q: sin(2x) dx+cos(3y) dy=0,y(π/2)=π/3

A: Given:

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A: Graph is given below:

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A: Given functions are

Q: y′=(3t2+4t+2)/2(y−1),y(0)=0

A: Click to see the answer

Q: What is a center of mass? a centroid?

A: To define centre of mass and centroid of an object.

Q: A young person with no initial capital invests k dollars per year at an annual rate of return r. Ass...

A: The rate of change of the sum is equal to the percentage of the sum at that time plus the amount he ...

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A: Consider the graph. The graph is symmetric across x = 0.

Q: A tank initially contains 100 gal of brine in which 50 lb of salt are dissolved. A brine containing ...

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for yo...

Q: determine whether the following statements are true or false 1. if z=f(y) and y= g(x) then dz/dx= d...

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Q: Assume that a spring does not follow Hooke’s Law. Instead, the force required to stretch the spring ...

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Q: The charcoal from a tree killed in the volcanic eruption that formed Crater Lake in Oregon contained...

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A: Formulas for the given type of forms is shown below:

Q: Find the centroid of the region in the first quadrant that is bounded below by the x-axis, above by ...

A: It is given that the centroid of the region in the first quadrant is bounded below by the x-axis, ab...