Find the length of the given curve. 4/3 3y2/3 X = -27 - 32

Q: The degree of the following curve may be 2 O a. None of these b. 1 O C. 3 d. 2

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Q: tind the D-E Sor the Following Family of curves y-ax+be

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Q: r = 3sin(Ɵ) Draw the curve, explaining it down to the smallest detail.

A: Given equation is r=3sinθ We have to draw the curve of r=3sinθ. First of all convert the given polar…

Q: Given the curve v = x3 – 3x find the stationary or turning point

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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: Find T,N and k for the curve:

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Q: Consider the curve y = 3x3, The sketch of the portion of this curve between x = - 1 and x = 8 is…

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Q: of the indicated portion of the curve. K.

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Q: Find the shortest distance between and the curve y=\x-1. Select one: V11 a. O b. O c. V13 O d. 2

A: Let (x,y) be the point on the curve where the distance to the given point is shortest. So the…

Q: Find the lines that are tangent and normal to the curve at the given point. x²y? = 36, (1,6) %3D

A: We will find first slope of tangent and then from the slop and tangent and point will find a…

Q: Find the length of the curve: 7= Scos 4. t2.

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Q: Find the exact length of the curve. 1sys2 8. 4

A: Solve the given

Q: find equations for the lines that are tangent,and the lines that are normal, to the curve at the…

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Q: Find the exact length of the curve. y? = 16(x + 1)³, 0 0

A: The given curve is y2=16(x+1)3,y&gt;0y=4(x+1)32 Now, differentiate y with respect to x.…

Q: Given the curve y = x3 + 3x, at what point is y' = y'' ?

A: As we know that, The Power law: ddxxn=nxn-1 The sum/difference rule: f±g'=f'±g'   Given: y=x3+3x And…

Q: A Moving to another question will save this response. Question 6 Find the length of the curve. x =t…

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Q: y = -x³/2,0 < x< 1 3.

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Q: Find the exact length of the curve 36y? (x² – 4)³, 2 0.

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Q: Consider the curve defined by xy^2-2x^3=2 for y=>0 See image for question

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Q: O Find asv mPtotes of the Following curves then graph them? Y= X2 +V 2-X

A: Topic:- function

Q: Which of the following curves pass through the point (1, 4)? c(t) = (t 2, 3 − t)

A: A point lies on a curve if it satisfies the equation of the curve. Substitution of the point into…

Q: Find N(t) and N(1) for the curve represented by r(t) = 3ti + 2t2j.

A: Given Curve  r(t)=3ti+2t2j We have to find N(t) and N(1) As we know that, Normal Vector is defined…

Q: 2 =(x² - 1)³/²,1 ≤ x ≤ 3

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Q: Find the the given curve e length of -64e4€ 27 3. 3y 34 32

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Q: No calculators. Find the exact length of the curve. y=2+2x³/2, 0≤x≤l

A: Given curve is y=2 + 2x32,  0≤x≤1 The objective is to evaluate the exact length of the curve. Length…

Q: Find the exact length of the curve. y = (1 + x2)3/2, 0 < x < 2

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Q: Given the curve shown below, determine if the slope of the curve at x = negative, or zero. 4 3 2 O…

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Q: Find the exact length of the curve. x = 4 + 6t2 y = 6 + 4t3 0 sts 4

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Q: I Discuss the properties of the curve and sketch fully: a) y = x? e-x

A: (a) Given- y=x2e-x To Find- The properties of the curve and sketch the curve.

Q: Given the curve y= x^3 - 4x + 1 . At what point on the curve have the smallest slope? * O (0,1) O…

A: The given curve is: y=x3-4x+1

Q: Determine the slope of the curve y= e^4x at the point x=O? * 1 -4

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Q: The given point is on the curve. Find the lines that are (a) tangent and (b) normal to the curve at…

A: This question can be solved by applying the concept of tangent and normal

Q: Find the length of the curve defined by from = 9 to z = 10. 2 y-4lm (()²-1) =

A: find derivative

Q: analyze and trace the given curve y = 2x3 + 3x2 - 12x + 7

A: Given:

Q: Which of the followings can represent the curve y=x? Choose all that apply. O O O 3t, 9t2>

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Q: Find the exact length of the curve. X √(y - 3), 16 ≤ y ≤ 25

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Q: The length of the curve defined by x =(v² + 2)E, y € [0,1]. Select one: none O 12

A: Arc length of the curve x=g(y), y∈[a, b] is, S=∫ab1+(g'(y))2 dy

Q: 6x 4. У3 y = х+3

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Q: 1. If x = -1 and y = 2, then what is the value of for the curve defined by e²y + xy = 3x² ? A. B.…

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Q: find equations for the lines that are tangent,and the lines that are normal, to the curve at the…

A: Solution:- The given curve is  x+xy=6  ......(1) and point (4,1) we have to find equation of the…

Q: 6- Which of the following is the shortest distance from the point (15, 0) to the curve y = /6x ? a)3…

A: 5

Q: 7. Find the points of intersection of the following curves and draw the figure. x? – 3y = 0; x² + 2…

A: We have to solve these two equations to find intersection points of these two curves.

Q: Find the exact length of the curve. y ‹ = ²(1 + x²j³/2₁ 3/2, 0≤x≤ 5

A: The objective of the question is determine the length of the given curve.

Q: r= g° ,0<g<\5

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Q: Find the inflection points of each of the given curve.  4y = 3x4 – 16x3 + 24x2

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Q: a) y = x? e-X

A: We have to discuss properties of the graph

Q: Find the length of the following curve. y=(1/3)(x^2 + 2)^(3/2) from x=3 to x=9

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Q: d the exact length of the curve. =√y (y - 3), (y - 3), 4 ≤ y ≤ 16

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Q: analyze and trace the given curve y = x / (1 - x)2

A: To solve the following problem

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.