Find the acute angle that the curve y = 1 − 3x3 cut the x axis.

Q: Find the r value of the point on the curve y = 3x + 2 closest to the point (1,0). Evaluate /(-글 +…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: tind the domain and range of y: sech X find the derivahive of

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Q: x = t3 − 12t,    y = t2 − 2 find d2y dx2 and for which values of t is the curve concave…

A: We find dx/dt and dy/dt.

Q: The function f(x, y) = sin(/3x² + 3y²) corresponds to plot [ Select ]

A: Find your answer below

Q: The curve has an equation of x = y^3, find the radius of gyration with respect to the x-axis. * 0.89…

A: Given curve is x=y3. We have to find the radius of gyration with respect to the x-axis. Since, no…

Q: : 6x² perpendicular At what point is the tangent line to the curve y°: to the line x+ 2y – 4 = 0?…

A: Explained below

Q: Find the length of the curve y = x2, 0 ≤ x≤√3/2.

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Q: Find the point in the first quadrant on the curve y = x + x - l closest to the origin.

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Q: Find the acute angle between the curves xy = -4 and y2 = 2x  If the correct answer is a =…

A: Given xy=-4 and y2=2x

Q: given curve about the x-axis. 1. y = 7x, 0 < x <1

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

Q: Find the point on the curve y2 = ;(x+1) which is nearest the origin.

A: We have to find the point on the curve y2=52x+1 which is nearest the origin.

Q: Find the exact length of the curve. y? = 64(x + 5)3, 0sxs1, y > 0

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Q: The x coordinate of the point of intersection between the two curves Y = e2lx and y = 1 is

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Q: Sketch the ff curves: a) Y = x2 ex 1+lnx b) Y = c) Y= (x²–4)2

A: Given: a)y=x2e-xb)y=1+lnxxc)y=x2-42x-4

Q: Find the length of the curve x y? – 2y, 0< y < 2.

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Q: (d) Find the points on the curve x'y = 60 nearest the origin.

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Q: Find dy/dx and d2 y/dx2 , and find the slope and concavity (if possible) at the given value of the…

A: Given: x=θ-sinθ, y=1-cosθ, θ=π We know that dydx for given expression is given by dydx=dydθdxdθ…

Q: Find the length of the curve, L. y = 16 (a + 3)", 0s s1. y> 0

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Q: Find the exact length of the curve y=1+6x% for 0<xsl

A: We have to find the exact length of the curve y=1+6x32 for 0≤x≤1.

Q: find the eauatjo aof the nor ma l to the curve 2. (x + 3)?y =3y-3x2

A: For any curve y=f(x), slope of tangents and normal at any point x1, y1 can be given by mT=dydx(x1,…

Q: Find the point on the curve y2 =;(x + 1) which is nearest the origin.

A: If (x, y) is any point on the curve nearest the origin then the square of its distance from the…

Q: The x coordinate of the point of intersection between the two curves y = e14 and y = 1 is =0 (Write…

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Q: Find the point on the curve y2 =(x+1) which is nearest the origin.

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Q: Find the point on the curve Y = √x closest to the point (3,3)

A: Given the curve is  y=x So the coordinates of any point in curve is given by x,x The distance…

Q: No calculators. Find the exact length of the curve. y=2+2x³/2, 0≤x≤1

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

Q: The line y=x+b is tangent to the graph of y=x1/2 at the point: P=(a,a1/2 ). Find P and determine b.

A: Given, The line y=x+b is the tangent of the graph y=x12 at the point P=a,a12

Q: Find the slope of the tangent to the curve y = 3e^(2x) at (0,3)  a. 3  b. 2  c. 6  d. 12

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Q: Find the exact length of the curve. x = 6 + 3t?, y = 2 + 2t3, 0 sts 5

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Q: Find the length of the curve. 5 17) y = 3x3/2 from x = 0 to x =- 335 335 B) 162 335 A) 243 D) 1 3

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Q: Q3/ Find the angle between two curves: 3 x2 , y = x² y = 2

A: Please see the answer in step 2

Q: For the curve y = ax3 + bx2 + 12x -7, what values of a and b will make the tangents to the curve at…

A: given  y=ax3+bx2+12x-7a=?b=?

Q: The slope of the curve when x=e is y = (In 2x)?

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Q: The equation of the curve is y? = x' + 8x. Find the x-coordinates where tangent lines are vertical.

A: We are given equation of curve  Y^2 = x^3+8x We have to find points where tangent lines Are vertical…

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

A: Length of the curve  =∫ab 1+f'(x)2 dx .

Q: xy = -4 and y² = 2х

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Q: Find the length of the curve x = (y3/33) + (11/4y) on 3≤y≤5.

A: Consider the given curve f(y) and find the derivative w.r.t y.

Q: Find the rectangular coordinate equation for the curve x= cost and y=1-sin2t for 0 greater or equal…

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Q: Find the coordinates of the point/s on the curve y = 2x? which are closest to the point (9,0).

A: We have to find the closet point to the point    (9, 0)

Q: Q. Find the length of the arc of the curve f(x) =+3,

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Q: Ex. 2: Find the length of the 2/3 curve

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Q: The curves x=y²and x = 2 y – y?

A: Since you are asking multiple questions. As per our guidelines, we are supposed to answer only one…

Q: Find the equation of the lines tangent to the curve x2 + y2 = 4 and parallel to the y-axis ? O A. X…

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Q: Find the length of the curve 3 y = x7 – 2 from x = 0 to X = 4.

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Q: Find the points on the curve where the tangent is horizontal or vertical. r = t - 3t, y = t?- 3.

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Q: A ski run follows the curve of y = 0.01xf-0.8x + 16 from x=0 m to xE 40 m What is the angle between…

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Q: The curve has an equation of x = y^3, find the radius of gyration with respect to the x-axis. * O…

A: The curve has an equation x=y3 K=IxA K= Radius of gyrationIx=Moment of inertia/Secon moment of…

Q: Find the angles at which the curve y=x3−x intersects the x-axis.

A: The angle at which curve intersect the x axis is determined by the angle of slope of tangent to the…

Q: Find the angle of intersection between the curves y = x- +1 and y = x+x-

A: y = x2 + 1,y = x+ x-1Points of Intersection;x2 + 1 = x+1xx(x2+1) =(x2+1)x = 1y = 2point of…

Q: The x coordinate of the point of intersection between the two curves 12x y = = el2# and y = 1 is x =

A: Our Aim is to find the x coordinate of the points of intersectionbetween the two curves y=e12x 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.