If U=[0 00 00012 34 5677777 7], the number of points consisting the B-spline curve are:

Q: Let C be the line segment joining A(1,1,1) to O (0,0,0). A parameterization

A: Given that A(1,1,1) and O(0,0,0) Find a parameterization

Q: Let {y;: t = 1, 2, ...} follow a random walk, as in (11.20), with yo = 0. Show that Corr(y, y;+h) =…

A: It is known that if yt follows random walk, then it can be written as yt = yt – 1 + et, forl all t =…

Q: In  the givne equation as follows ,determine the open t-intervals on which the curve is concave…

A:

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.

A:

Q: Let C be the curve y = 2.5 In (6.25 – x²), for – 1.2 < x < 1.6. A graph of y follows. 4.6 4.5 4.4…

A: Here, y=2.5 ln6.25-x2. So,         y'=2.5ln6.25-x2'           =16.25-x26.25-x2'    =2.5·16.25-x2-2x…

Q: 13- Find the length of the curve a) r(t) = 4costi + 4sintj³ + 3tk³ 0< t < 3n b) r(t) = 4ti + 4tj¬ +…

A: Please refer the image,

Q: 5) Let à = psin(4)ū, + p² Ug Evaluate f Ã. dl given that L is the contour of the following figure.

A: Let A→=ρsinϕu→ρ+ρ2u→ϕ we have to evaluate ∮A→.dl→

Q: Let C be the curve y = 8/a for 2.1 < x < 3.8.

A:

Q: Find the exact length of the curve. v= In(1 – x²). y 0 <x < 1 In(|3|) - 8.

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

Q: is absolutely and uniformly conyergent for all vlues of x an t in the circle 121 <B-¹

A:

Q: Consider the closed curve C, which is th

A: Given, the closed curve C, which is the image of the path…

Q: / Fit a curve of the form y = ax + bx² to the data

A: Given,    x 1 2 3 4 5 y 1.8 5.1 8.9 14.1 19.8 To find             y=ax+bx2…

Q: Compute the value of ( G. dL for G = 2ya, with A(1, -1, 2) and a) straight-line segments A(1,-1, 2)…

A: Given the line integral ∫APG·dL for G=2y,0,0 with the initial point A1,-1,2 and P2,1,2 using the…

Q: 2. Let z₁ and 2₂ be two distinct points in CU{∞} that are symmetric with respect to a circle I.…

A:

Q: Find the are length of the polav Curve r=3° from o-0 to 0= 1

A: Solve the following

Q: 8how that the square of the leng point on the curve by = (x + a)° , length of the subnormal at that

A: Subnormal and Sub tangent: Allow y=f(x) to be the differentiable curve at point P. Let the tangent…

Q: find z such that 5.2% of the standard curve lies to the left of z.

A: Probability = 0.052 Finding the value of z corresponding to p=0.052= -1.62576 ( From Excel…

Q: Find the T(t), N(t), B(t), and K(t) of the following space curves:

A:

Q: Compute the length of the curve over the given interval. r(t) =〈3t, 4t − 3, 6t + 1〉, 0 ≤ t ≤ 3

A: Given rt=3t,4t−3,6t+1,  0≤t≤3Formula→Arc length=∫abr't dtr't=f't2+g't2+h't2    rt=xt,yt,zt

Q: Compute the length of the curve 3ti – 6tk over the interval 8 <ts 18.

A:

Q: (1) whot is 'the value of n that the xyn=c are per pendicular Curves とっ the Curves 1- mx

A: 1) What is the value of n so that the xn+yn=c curves are perpendicular to the y=x1-mxcurveGiven…

Q: 16. Obtain the toigonometric fouries seajes for A fit) > wt 277

A: The given image is of sine wave form. Here, period T=πand so, w0=2πT=2ππ=π

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 U=[0 0 0 000123456777777], the number of points consisting the B-spline curve are

A: Given knot vector is, U=0 0 0 0 0 0 1 2 3 4 5 6 7 7 7 7 7 7 The knot vector is formed according to…

Q: Use Simpson’s Rule with n  =6  to estimate the length of the curve x  =t - et -6&lt;t&lt;6

A:

Q: The necessary and sufficient condition for a given curve to be a plane curve is that t = O at all…

A:

Q: Determine whether the work done along the path C is positive, negative, or zero. y

A: The work done along the path C is

Q: 1. Prove that given a line € and a point P not on e, there exists a line through P perpendicular to…

A: Explanation of the answer is as follows

Q: (b) Suppose C is a curve of length N, and ||F|| < M, where M is some positive number. Prove that F.…

A:

Q: 3e) if c is any Simple Closed Curve, evaluate f dz, if ü7is out side (ii) 7 is in side

A: We will solve it by Cauchy Residue Theorem ∫f(z) dz = 2πi×R where R is the Residue of the…

Q: | Let w=z² Find the image of the first quadrant in Z-Plane 2

A:

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

A:

Q: Which of these best describes T?

A:

Q: Let C be the part of the curve oriented counter- clockwiso Evaluate xtyal with Fidr,

A: Here we will use stokes theorem to find given line integral for vector F  ∫CF.dr=∫∫SCurlF.ds S is a…

Q: he accompanying data file contains 10 observations with two variables, x1 and x2. picture Click…

A: x1 x2 6.63 0.85 4.89 0.19 11.24 1.47 23.98 0.74 3.89 2.36 33.99 0.8 4.56 1.64 10.42…

Q: If z = x + jy, find the equations of the two loci defined by: (a) |z – 5| = 4. (b) arg (z + 3) = 5.…

A:

Q: Consider the path r(t) (14t, 7t, 7 In t) defined for t > 0. Find the length of the curve between the…

A: Given - r(t) = ( 14t, 7t2, 7lnt )  defined for t&gt;0 To find - The length of the curve between the…

Q: A Bezier curve is defined by PO (0,0), PI (2,5), P2 (5,5) and P3 (7,0). Sub divide the curve at u…

A: We will get only one point as we have only one value of u. The given points are P00,0, P12,5, P25,5,…

Q: the compler pleme Sketcl given by the Curve in Iz-31=12+3il %3D

A: Just use definition of modulus of a complex number.

Q: be a normalize s in general for x | ≤||x|*||y|| e or disprove it eans multiplicati

A:

Q: that H(m m). Show

A: Given function is: Hm=3m-2 We have to find the inverse function H-1m. Let Hm=y Then we get,…

Q: an implicitly de fined curve is gren below. 3x+4y²+3xy-24

A: Given In part (a) find the derivative of equation with respect to x. This is the required answer.

Q: Show that F. dr is independent of its path, given that

A:

Q: Consider the path r(t) = (4t, 2t², 2 In t) defined for t > 0. Find the length of the curve between…

A:

Q: Suppose y = In (Inx). What is dyldx? *

A:

Q: Let f(x, y, z) = 114xz – 6y and let C be the curve given by r(t) = for 0 <1< 2. Compute fe f ds.…

A: Iine integral over the surface

Q: 1- Fit a least-square geometric curve y = ax to the following data 2 3 4 5 y 27.8 62.1 110 161

A: We have to find Geometric Curve using least square method.

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.