Consider the inmplicitly defined curve xy +3x2 4. %3D O Verify that the point (1, 1) is on the curve.

Q: (b) Investigate where the curve y = xy4 - x² is concave up and concave down?

A: Given curve is y=x4-x2 find the concavity of the given curve

Q: Find the length of the curve on y=2x^(3/2) from x=0 to x=1

A: Explanation of the solution is given below...

Q: Consider the curve segments: 1 - to x = 4 and 3 1 to x = $1: y = x² from x S2: y = Vx from x = = 16.

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Q: 2 The length of the curve y = 312 between x = 0 and x = 1 is 3 %3D %3D

A: Answer is 4√2/3 unit.

Q: 3) Find the exact length of the curve: x = y = In(1+t); 0<t<2.

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Q: Find the length of the subtangent and sub-normal at a point of the curve y= bsin(x/a)

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Q: Use the IVT to prove that the curves y = x2 and y = cos x intersect.

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Q: Find the length of the curve y =x/2 from x = 0 to x = 3.

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Q: Find the length of the curve y = V4t2 – 1 dt, 1<x<2 O 3 O 8 O 104 3. O 15

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

A: The length of a curve means the arc of the length of a curve. The arc of the length of a curve in…

Q: Find the exact length of the curve. x =Vy ( - 3), 1sys 25

A: given: x=13yy-3

Q: Find the arc length of the graph of the function y=2x32+3y=2x32+3 over the interval [0,9][0,9].

A: Here we have to find the arc length of the graph of the function y= 2x3/2 +3 over the interval [0,9]

Q: Eliminate the parameter to express the curve in the form y = ƒ(x) . x = 4t2, y = t3 - 1

A: We have given curves; y = ƒ(x) . x = 4t2, y = t3 - 1

Q: For a χ2-curve with 22 degrees of freedom, find the χ2-value that has area a. 0.01 to its right. b.…

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Q: tind the point on the curve y=Jx that is closest to the point (3,0).

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Q: consider the curve y=x^2-4x+2 show that the normal to the curve at the point x=1 is 2y-x+3=0

A: TO SHOW THE EQUATION OF NORMAL AT x=1 IS  '2y-x+3 =0' GIVEN y = x2-4x+2 EQUATION OF NORMAL AT x=1 is…

Q: Find the exact length of the curve over the given interval. 1 along 1 < y < 2. 8 4y2 ' ||

A: Find the length of the given curve

Q: For a χ2-curve with 19 degrees of freedom, find the χ2-value that has area a. 0.025 to its right. b.…

A: a) Degrees of freedom is 19 The chi-square value that has area 0.025 to its right is given below:…

Q: The Normal to the curve 2x2 – y? = 1 at the point (1,1) is: %3D 3 y =-*+ y =x+ y = 2x + 1 %3D P. y =…

A: To find The equation of normal to the curve 2x^2-y^2=1 at the point (1,1)

Q: 5. Find the length of the curve given by y= Vt* – 1 dt and 1<x<2.

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Q: compute the length of the curve over the given interval.  r(t) = (2t2 + 1, 2t2 − 1, t3), 0 ≤ t ≤ 2

A: Length of a curve is also like computing distance between two points but with the restriction that…

Q: If lx + my = 1 touches the curve (ax)" + (by)" = 1, show that %3D )+) = 1.

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Q: Find the length of the curve y = x/2 from x =| 0 to x = 3.

A: We have to find out the length of curve.

Q: Find the point on the curve y = Vx closest to the point (1,0).

A:

Q: 8.) Find the exact length of the curve y= over the interval (0.4]. 2 %3D -

A: Given,          The exact length of the curve y=x22 over the interval 0,4 .

Q: B. Find the length of the curve y= x2 from x = 0 to x = 7.

A:

Q: Find the length of the curve given by S(x) = (a -) defined on the interval (1, 2].

A: Consider the given curve:

Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

Q: Find the length of the curve y = V- from z =1 to r = e. 3

A:

Q: Find the length of the curve y = S Vcos t dt, 0 <x<n.

A: Given; The curve y=∫0xcost dt,      0≤x≤π .

Q: Find the tangent plane to the graph of **yz +z'e* -y² = 5 at (1,3,2).

A:

Q: Find the length of the the interval -2sxs-1. y = L, V3t² – 1 dt curve in

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Q: Find the length of the curve y = 4 1 between x 1 to x 2. %3D &x2

A: It is length of curve.

Q: Find the required x-value. For a x2-cu -curve with 27 degrees of freedom, find the X-value having…

A: Given data:Degree of freedom  =27 Area to the right  = 0.01

Q: Consider the implicitly defined curve xy? +3x2 = 4. %3D Verify that the point (1, 1) is on the…

A: Consider the following curve: xy2+3x2=4 Substitute x=1 and y=1 in the above curve:…

Q: find the length of the curve on the given interval: y=1/3(x^2+2)^(3/2), [0, 1]

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Q: 3. Discuss how to evaluate f () dz , where C is a simple closed curve C=10 enclosing the origin.

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Q: 2. Find the area of the smaller loop of the curve r = = 3( 1- 2cose)

A: We will solve the following

Q: Consider the sope old shown obove For the solution that sotrios y(1) -0.75, skotch the solon curve…

A: Given the slope field along with a point on the curve 1,0.75. We sketch a curve that is passing…

Q: Find the exact length of the curve. x = 8 4y2' 1sys 2

A: Given, x=y48+14y2,1≤y≤2

Q: Find the length of the curve y Inx at (2<x< 4)?

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Q: The area bounded by the curve y = 6z and the lines a = 5 and z= 8 above the T aris is 234.00 square…

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Q: Evaluate | 9+x* dx+xy*dy along the positively oriented curve C where the C is the boundary of the…

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Q: Find the orthogonal trajectories of the given family of curves y? = tcx 1-cx

A: The orthogonal trajectory is the family of curves that is perpendicular to the given curve. The…

Q: FInd c and d so that the curve y = x3+ cx2+d will have a relative extrema at (2,5). Find other…

A: Maxima or minima: Let f(x) is any function. 1) Evaluate f'(x) = 0 for critical point. 2) Evaluate…

Q: 3) Find the exact length of the curve y = x² – In x for 1< x < 2. 1„2

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Q: What is the length of the -3< x S3 segment of the y = v36 – x2 www vwwb w e curve?

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Q: what is the length of the curve y=1-cos(x) from x=0 to x=4pi

A: The given curve is  y = 1 - cosx dydx=0 - (-sinx)  =sinx