Let C be the curve defined by x? – y? = 1. Consider all points (x, y) on curve C where a > 1 and y > 0. Which of the following statements provides a justification for the concavity of the curve? The curve is concave down because y" = -エく0. The curve is concave up because y" = > 0. The curve is concave down because y" = く0. The curve is concave up because y" = > 0.

Q: Find the set on which the curve is concave upward. Answer (in interval notation): | 2 y = ₁² 1²+ 3²…

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

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Q: Sketch the plane curve r(t) = 2ti − 3tj,  and find its length over the given interval [0, 5]

A: Given plane curve: The parametric form of vector valued function is It is the equation of line in…

Q: Let C be the closed curve indicated in the diagram. Use Green's Theorem (2,1) (o,i) (x² + y?, y³ +…

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Q: A________ is the set of points P in the plane such that the ratio of the distance from a fixed point…

A: The conic section is known as the set of points, in which the curve of any of the conic, that are,…

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: 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: 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: Use Eq. (5) to find the point P nearest to Q = (2, 1, 2) on the plane x+y+z=l.

A: Consider the provided information, Find the point P. The normal vector to the plane is 1,1,1. And…

Q: ) Find an equetionof tue tenyent line to the greph of d= In(x') at the point (l,0). Angwery8 a) y*-5…

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Q: O Find all values of t such dhat dhe dangent line a CI()=<E,tit3-37 is parallel to xy-plane.

A: Given:-r→(t)=&lt;t, t, t3-3&gt; and the tangent line parallel to XY-plane (z=0)now,tangent vector on…

Q: Which of the following expressions gives the length of the curve defined by R(t) = tij +In tk…

A: We have to find arc length expression for the given vector function. Given is the curve…

Q: Let C be the curve in space given by the following parameterization. Then d + 2dy +adz is equal to…

A: Given ∫xdx+2dy+zdz = ∫(xi+2j+zk).(dx i + dy j + dz k) = ∫F.dr Here F = (xi+2j+zk)…

Q: Let F(x, y) = x²e* i+ 60x²y² j, and let C1 denote the curve consisting of the line segment from…

A: Given:- F→(x, y)=x2exi→+60x2y2j→To calculate:- ∫C2F→.dr→where C2 is the line segment starting from…

Q: Show that the following set is a curve: K = {(x, y) E R² | xy – x = 1}. Briefly explain your…

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Q: Let θ be the angle between the line y = mx +b and the x-axis. Prove that         m = tan θ.

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Q: 4- Find the length of the curves in Exercises. 1. y = (1/3)(x² + 2)³/2 from x = 0 to x = 3 3. x =…

A: for a function of the form y=f(x) length of the curve from x=a to x=b is: L=∫ab(f'(x))2+1dx and for…

Q: 4- Find the length of the curves in Exercises . 1. y = (1/3)(x² + 2)³/2 _from x = 0 to x = 3 3. x =…

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

A: Solve the following

Q: Find a parameterization, x = x(1), y = y(t), tE [0, 1], for the line segment from (2, -1) to (5, 5).

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Q: By using Green's theorem evaluate (4.ry – y') dr + (x + 3ry) dy where C is a closed curve starting…

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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: c) GIVEN: T is the midpoint of ME & ZG=ZJ PROVE: Tis the midpoint of GJ STATEMENT

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Q: Find the length of the curve. 30) x = 3 ty 3/2 - y 1/2 from x = 16 to x = 25

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

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Q: c) By using Green's theorem evaluate OUIM GUTM U where C is a closed curve starting from the origin…

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Q: Examples Fid io av ed of the vegim borodkl by ke vegin Cuve and line hy mlars of double ifegrafin,…

A: Please refer the attached image for complete solution.

Q: Let C be the line segment connecting 0 to ni. Then f. 1-e22 dz = a. 0 b. -0.5 + ni C. πί d. None of…

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Q: 14. Determine y = 3x EDI DITED Ee, if any, the tangent line t EDBYS BY JO JOHN OHN GI) = 2x³ – NGIL…

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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: Let y = [3] and u = [2] to the line through u and the origin. Compute the distance from y

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Q: Let C2 be the curve defined by R(t) = (t² +t + 3, 4t – 5, 2+ t – t2), t e [0, 1]. %3D | (x + y+ 2)…

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Q: Find the length of the curve. x = 4t, y = 2/3t 3/2, 0 ≤ t ≤ 9     a)61/3     b)242/3     c)61/2…

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Q: consider a curve r(t) = 2t³ i+ 2t j+v6t² k calculate the length of the curve in the interval 0 st 3

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Q: Find the length of the curve 24xy = y + 48, Select one: 85/85-8 243 80/10-13/T3 27 O None of these

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Q: (is)Find the eguakion af the line tangent to y=ro* át (!,10')

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Q: Compute the length of the curve r(t) = 3t i+ 2tj+ (t² – 2) k over the interval 0 <t < 5. HINT: use…

A: Given problem is :

Q: Determine the length of the curve y = x +x in the interval 1 <a <2. %3D 59 24 O 2.86 O 3.01 127 50

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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: ind the the exact length x = et – t, y = 4e/2, |

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Q: Q5. Prove that the circle {(r, y), x² + y? = 1} is not homeomorphic to the interval [-1, 1].

A: Here we can prove this question using topological property connectedness.

Q: 12. Let fc A. Find the linear a pproximer X= 7, In uther word's, find the tu, to the curve y= Fcx)…

A: Introduction: A tangent line is a line that simplest touches a curve at one factor and does now no…

Q: Let C be the curve connecting (0,0) to (9,3) to (-3,3) to (0,0) using straight lines. Evaluate (sec…

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Q: apply stok's Theorem to evaluate (Ydz +7dy+ xdz) whereCiB the curve of intersection of x²+ y²+z² =…

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Q: 4- Find the length of the curves in Exercises. 1. y = (1/3)(x² + 2)³/2 _from x= 0 to x = 3 3. x =…

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Q: Let C2 be the curve defined by R(t) = (t² + t + 3, 4t – 5,2 +t – t²), t e [0, 1]. Evaluate | (x + y+…

A: The solution is given as