I Discuss the properties of the curve and sketch fully: a) y = x? e-x 1+2nx b) y = =

Q: Find the length of the curve. x = 4, y = 3/2, 0 st 0st <9 242 61 2

A:

Q: 1. Center: 2. Radius: 3. Diamete 4. Chord: E. H 5. Tangent 6. Secant:

A: Given:

Q: 5. Trace the curve r = sinocos³o.

A: Given curve: r=12sinθ cos3θ

Q: = y}2 /3 – y!2, 9 < y< 81 %3D

A: By using length of the curve formula, we calculate the required length of the curve.

Q: Refer to the figure above. In the upward-sloping portion of the curve that connects points A, B, and…

A: Answer:- Independent

Q: 1. For each curve, construct dr. • Let C1 be r? + y? = 16 • Let C2 be y = 5 – 2x • Let C3 be r = 2 –…

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Q: Ex 3 identify the equarion of a line a) parallei that is é b) perpendicular y= x-2 through ly,-1)

A:

Q: Find the exact length of the curve a 1+ 3t", y = 4+2t", 0 <ts1.

A: Exact answer is 2(2√2 -1)

Q: Evaluate x ds, where C is a. the straight line segment x =t, y =. from (0,0) to (6,2) b. the…

A: We need to evaluate ∫Cx ds

Q: sketch the given curves together in the appropriatecoordinate plane, and label each curve with its…

A: Draw graphs of y=ex and y=1ex

Q: Find the length of the curve. r(t) = √√2ti + etj+ek, 0≤t≤7

A:

Q: The speed (mph) and the stopping distance (ft) of a travelling car are given as follows. Speed…

A: Use the Excel and Perform the Regression. Followings are the Steps to perform the Regression 1) Open…

Q: Find the exact length of the curve. x = et − 9t,    y = 12et/2,    0 ≤ t ≤ 2

A: Note that:Arc length formula = ∫abdxdt2+dxdt2 dt                   where , a≤t≤b       Given,…

Q: Find the exact length of the curve. x = 8 + 9t?, y = 3 + 6t, 0 sts4

A:

Q: Find the length of the curve. Vzti + e'j + e-tk, 0 sts 3

A: Given data:     The given expression is: r(t)=&lt;21/2ti+etj+e-tk&gt;. The given limits of t are:…

Q: Find an equation for the tangent plane to the surface 2? – ry? = 0 at the point G, 2, 3)

A:

Q: Find the exact length of the curve. 36y? = (x2 – 4)3, 4 0 23.335

A:

Q: Evaluate x ds, where Cis с a. the straight line segment x = t, y = = 737₁1 3' b. the parabolic curve…

A:

Q: What is the length of the latus rectum for the curve, (x + 3)2 + 4(y – 1)² = 4 а. 2 O b. 1 О с. 4 O…

A:

Q: If a curve C is given by r(t) = ⟨t, t2⟩ , what is | r'(t) | ?

A:

Q: Can two spheres a) be internally tangent? b) have no points in common?

A: a) The answer is yes. In fact, if the distance between the centers is equal to the difference of the…

Q: Please please type by computer  Describe how reversing the orientation of a curve C affects the…

A: The curve C is given by r(t)=x(t) i +y(t) j, where a≤t≤b. Now, the reversing orientation gives the…

Q: A simple curve is shown below. Given: A and T (tangent distance) Required a.) E b.) M c.) Length of…

A: A simple curve is given. Given - Deflection angle=∆Length of tangent =T To find - (a) EE is length…

Q: zejz dz, 22 – 5z +4

A:

Q: Explain the steps required to find the length of a curve x = g1y2 between y = c and y = d.

A: It is given that x=gx for c≤y≤d.

Q: Find the length of the curve. 2,3/2,0 st s9 x= 4t, y 3 61 242 2 3 O 2. seçenek 4. seçenek 122 61 3 3…

A: We can find the arc length as below

Q: Find the 0lar eauatiDo for the curve represented by the given Cartesian euation.

A:

Q: Find the exact length of the curve. x = et − t,    y = 4et/2,    0 ≤ t ≤ 2

A:

Q: Evaluate ∫C x ds, where C is the parabolic curve x = t, y = t2, from (0, 0) to (2, 4).

A: Given: Parabolic curve x=t, y=t2 from (0,0) to (2,4)

Q: Sketch the following curves. 33. y = 2x + 3x2 + 1 %3D

A:

Q: Find the exact length of the curve. x = et − t,    y = 4et/2,    0 ≤ t ≤ 5

A: We will use arc length formula to solve this questions

Q: Evaluate ∫с (x+y^1/2) ds, curve is given by figure 2

A:

Q: The curve assumed by a heavy chain or cable is: y = C cosh %3D If C = 50 Calculate; The value of…

A:

Q: Find the cylinder surface determined by Curve 4x?+9g? -36=0 and d= ( 1, -1. 32 line.

A:

Q: Find the length of the curve. Vzti + etj + e-tk, Osts 3

A:

Q: Prove that the curve given by the equations x=R(cost+tsint),y=R(sint−tcost) is the involute of the…

A:

Q: Find the olar eauatiDo for the Curve represented by the given Cartesian eawation.

A:

Q: Find the exact length of the curve. x = et + e=t, y = 5 – 2t, 0st< 4

A: The solution are next step

Q: nath A = 30, B = 20, C = 11, D = 22. 3. Discuss how to evaluate Z enclosing the origin. dz, where C…

A:

Q: Find the curve length 1 +2)?,0< y < 4 %3D 3

A: Given that, the function is x=13y2+232 and the interval is 0,4. Note that, the arc length of the…

Q: Find the length of the curve. 2ti + etj + e k, 0<tS 4

A:

Q: At what part of the curve 2x2 + y? = 8 does it assume the highest value?

A:

Q: What is the length of the curve I=1+32, y = 4+2t, (0 <t<1) ?

A:

Q: The siope of a line tangere to the curve y=fx)at(3 4) 0f iz cists) equais

A:

Q: 9t4 – 1dt, 1< x < 5 y = L = %3D

A:

Q: At what points do the curves y=x2 and y=√x intersect? Find the angles of intersection between the…

A:

Q: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = et, y = e-t

A:

Q: Explain how to find the length of the curve                         r(t) = ⟨ƒ(t), g(t), h(t)⟩, for a…

A: To Determine: Explain how to find the length of the curve Given: we have rt=&lt;f(t),g(t),h(t)&gt;…

Q: The length of the curve z=z(t)=5e", Ostsa is а) 12л b) л c) 157 d) 2

A: Sol :-                Are length in (a,b) if functions are                               x(t) , and…

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.