Find the length of each of the following curves: %3D %3D x (ey + e) from y = 0 to y = 1

Q: find the domine of the function y(t)=sin 4t

A: Consider the given function: The domain of a function is the set of input or argument values for…

Q: Find the points on the curve xy2 = 54 nearest the origin.

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Q: 1) Find the legth of the curve; y = e from x =1 to x = 2.

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Q: Given æy + cos(xy) + 9x = 7, answer the following: Write the equation of the normal line to the…

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Q: Find the length of the curve y=Arc sin e^x when y= pi/6 to y=pi/2

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Q: Find the length of the curve y2 = ln x, -1 ≤ y ≤ 1.

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Q: Find the area A of the largest rectangle that can be inscribed under the curve of the equation below…

A: Given y=e-x2

Q: For what values of a are the graphs of y = a* and y = 1 +x tangent at x = 0? Enter the exact answer.

A: Please see the explanation below

Q: 1) Find the length of the curve; y = e" from r= 1 toI = 2.

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: Find the curve length of the given functions in the given interval

A: Find dx/dt and dy/dt using product rule.Then find (dx/dt)^2 and (dy/dt)^2.

Q: Given the equation x In(y) = z Arctan(3*y). Assuming z as a function of variables a and dz find

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Q: Find the equation for the curve f (x) at the point (x, y) meet the following conditions dy / dx = 4x…

A: A curve is a function with equation of the form y=f(x). A differential equation is an equation in…

Q: Find dy/dx and (d^2)y/dx^2, and find the slope and concavity (if possible) at the given value of the…

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Q: The line y = mx + 1 is a tangent to the curve y2 = 4x .Find the value of m

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Q: Find dy/dx and dy/dx². x = e, y = tet For which values of t is the curve concave upward? (Enter your…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: For the implicitly defined curve: cos(7y) 5y sin(x) dy (e.g., find y' ). dx a. Find a formula for dy…

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Q: Find the length of the arc of the curve in the given range, x3 + 3 1 у %3D25х + 5x2 + 0 <x< 5 4(x +…

A: The arc length of the curve is given by integral:

Q: Find the D.E. for each of the curves determined by the condition that at each point (x, y) ,   The…

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Q: Find the length of the are of the curve п x=e' sint , y=e' cost from t-0 to t=:

A: Given: x=etsint, y=et cost from t=0 to t=π2

Q: At what point(s) does the curve given by x = 2 − t^2, y = t^2 + 2t have a horizontal tangent?

A: Solution :- For the curve to have horizontal tangent  Put dy/dt  = 0  The whole procedure is shown…

Q: The families of curves represented by the solution of the equation dy dx for n = - 1 and n = + 1,…

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Q: Find the exact length of the curve. 43. x = t sin t , y = t cos t , 0 ≤ t ≤ 1

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Q: x = e* + e=t Find the exact length of the curve for – 2 <t < 0 y = – 7 – 2t arc-length =

A: We use the formula of arc-length of a parametric curve to answer the given question

Q: Find the lengths of the following curves: e. x = 8cost + 8t sint and y = 8 sin t – 8t cos t, 0stsn/2

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Q: Determine the length of the curve of the following functions (x²*+ 1)} a, y=- from x = 1 to x = 4 b.…

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Q: Evaluate Sxy dx dy, over the region in the first quadrant given between the following curves -1 and…

A: Step:-1 Given that x216+y29=1---(1) and x4+y3=1---(2) Using graph, we can see intersecting point of…

Q: Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. (If an…

A: The given function is y2=ln(x)

Q: Given the equation r In(y) = z Arctan(3*y). Assuming z as a function of variable dz and y, find

A: The given equation is xln(y)=ztan-13zy ........................................ (1)  Here z =…

Q: Find the length of the arc of the curve x=e'sint , y=e'cost from t=0 to t= п b) d) 1

A: To find: The arc length of the curve: Given: The equations are x=et·cos t and y=et·cos t and the…

Q: At the given point, find the line that is normal to the curve at the given point. 6x <y - TT Cos y =…

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Q: Determine the length of the curve obtained from the graph of the function e +e=* f(r) = from r = -1…

A: We will find the length of the curve from the graph of the given function as shown below

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

A: The given curve is,

Q: A curve is defined implicitly by the equation x²+xy+y? =1 dy Differentiate implicitly to find dx

A: here we use basic differentiation form.

Q: Find the arc length of the graph of the function over the indicated interval. X = 3 Vyv - 3), 1<y s…

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Q: The slope of the tangent line to the graph of y =; I+1 when x = 1 is %3D %3D - 4 3/4 O 1 4. 1/2

A: y=xx+1 Slope of the tangent line is the derivative of the given function at the given point. So…

Q: Find the length of the arcc of the curve x=t2, y=t3 from t=0 to t=4.

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Q: dx L% = 1+ dy dy

A: Given equation of curve; y  = (x/2)3/2 , x = 0 to x = 2

Q: Find an equation of the curve that satisfies dy 33yr10 dx and whose y-intercept is 4. y(r) =

A: The given differential equation of the curve is, dydx=33yx10 Given that, the y-intercept is 4. That…

Q: y=Cx^2 and y=lnx find C where the graphs are tangent to each other

A: We have to find the value C.

Q: 10. Circles tangent to the X-axis. Amm. [1 + (y)*]° =[yy +1+(]".

A: Every function can be described through a differential equation. The differential equation defines…

Q: Find a dy + y dx, where C is the arc of the curve y = e* for 0 < x <7

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Q: If PQ and PR are tangent to OE in the given figure, find the value of x.

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Q: The curve y = sin'x has a slope of %3D Select one: a. at æ = ± O b. Never O c. at x = 0

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find, correct to two decimal places, the coordinates of the point on the curve y =sin x that is…

A: Given that y=sinx So coordinate point is x, sinx.

Q: Find the equation of the tangent to x = = VE , y = t – at the point where t = 4. Note: Sample format…

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Q: x = VE, y = t? – 2t; t = 16

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Q: If x = 10 cos 0 and y = 10 sin 0, find the total length of the curve swept out by the point (x, y)…

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Q: ind an equation of the tungent line to y= 45in2 X at point (i II

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Q: Sketch the graph of y = t + sin t for 0 ≤ t ≤ 2π.

A: The given function is y=t+sin t    for  0≤t≤2π. Sketch the graph of the above function as shown…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.