zdz where y is the straight line segment from 0 to 1+i is 1 0 i o -i O

Q: Find x so the distance between (x, 2) and (1, 5) is V13.

A:

Q: - 2ry? = 0, y(0) = -1. The interval I of definition os (D) (-∞0, 0).

A:

Q: Evaluate F.dr where F(x, y) = xry i+e*j and C is the line segment from (2, 0) to (4, 0). а) 0 b) 2…

A: Line integral

Q: y = vx , x = 4,y = 0 about the line x = 4. %3D

A: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

Q: Ex: Find the distance between the pt G(4₁-4,4) and the line x=2t₁ y=Z-3, z = at +2₂

A:

Q: 2. Let j = Find the point on the line y x that is closest to j. %3D %3D 26

A:

Q: Evaluate F.dr where F(x, y)-ny I+ej and Cis the line segment from (2. 0) to (4, 0). a) 0 b) 2 c) - 2…

A: Solved below...

Q: Which of the following gives the length of the curve y x2 + 2x from x = 0 to x = 5 ? (x2 + 2x) dæ I…

A: Length of the given curve will be

Q: Find length of the cardioid r-a03from 0 0 to 0 t %3D

A: To find Length of cardioid r=aθ3  where θ=0 to θ=π

Q: 2. Evaluate (x² + iy) dz, where C is the straight line from z = 1 to z = i.

A: to find  ∫Cx2+iy3dz,  where C is the straight line from z=1 to z=i proof using giving condition we…

Q: Evaluate (x+ y)ds where C is the straight-line segment x = 3t, y = (12 - 3t), z = 0 from (0,12,0) to…

A: We need to evaluate the integral along the given line. First eliminate the parameter t.

Q: Let C be the line segment connecting 0 to ni. Then f. 1- e22 dz = %3D a. 0 b. -0.5 + ni с. пі d.…

A:

Q: | Find fe(x² + y)i + 4y' j) dr where C consists of the three line segments from (4, 0, 0) to (4, 5,…

A:

Q: 1 The length of the curve y = x³ + x¹ from x = 3 to x = 4 is: a. b. C. d. 145 16 257 12 99 8 593 48

A:

Q: Evaluate F.dr where F(x, y) =xry i+e*j and C is the line segment from (2, 0) to (4, 0). a) 0 b) 2 c)…

A: use parametrization of a line segment and formula for the line integral.

Q: ALet f (2) = x² + iy² where x and y are the real and imaginary parts, respectively of z and C is a…

A: Complex integration

Q: Let f(z) = x? + iy² where æ and y are the real and imaginary parts, respectively of z and C is a…

A:

Q: 2. Find the exact length of the curve. y = 3 ,1 < x< 2 15+51

A: Find the exact length

Q: v(e -Y cos x) • dr, where C is the line from (0,0) to (2x, kn 7)

A: The fundamental theorem of line integral, also known as gradient theorem states that suppose a curve…

Q: Q: If the point (x, y) is equi distant from the points (a+ b,b-a) and (a-b,b+a). Prove that bx = ay.

A: Use given conditions to prove bx=ay

Q: Find the length of the curve r = 02 from 0 = 0 to 0 = 14.

A:

Q: Find the length of the curve. x=(y - 1) 3/2 from y = 1 to y = 4 O 7 O 10 21 2 O 1

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Q: Let f(z) = x? + iy² where x and y are the real and imaginary parts, respectively of z and C is a…

A:

Q: Find the exact length of the curve. X = Vу (у — 3), 16 <y S 25

A: First differentiate wrt y

Q: 3 Find the length of the curve y = x² – 2 from x = 0 to x = 4.

A: Given curve is y=x32-2 Upon differentiating we get dydx=32x12 We know that length of…

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…

A:

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 length of the curve. x = (v - 1) 3/2 from y = 16 to y = 25 O 4 61 O IK

A:

Q: Find ((x? + 4y)i + 4y j) · dr where C consists of the three line segments from (3,0, 0) to (3, 5,0)…

A:

Q: Find ((x + 4y)i + 4y j) · dr where C consists of the three line segments from (3,0, 0) to (3, 5,0)…

A:

Q: Evaluate F. dr along the line segment C from Pto Q. F = -8 xi+5y j; P(-1,0), Q(7, 0) F. dr i

A:

Q: Compute the length of the curve r(t) = (-4t, 5t — 3, -2t + 3) over the interval 0 ≤ t ≤9 L =

A:

Q: Which of the following is NOT a formula for finding the distance between two points on the…

A: Topic = Coordinate geometry 1st option is correct answer.

Q: The length of the curve y = r from r = 0 to r= 2 is A. V1+1®dr B. V1+ 3r² dr C. V1+*dr D. V1+ 9r* dr

A: Here I am attaching image so that you understand each and every step.

Q: Find the equations of the tangent and normal line 4x2 + y? + 8x + 2y = 20 at x = -3 %3D

A:

Q: 10. Evaluate (x – y + z - 2) ds where C is the straight-line segment x = t, y = (1 – t), z = 1, from…

A: Given C is the straight line segment , from (0, 1, 1) to (1, 0, 1) .

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

A:

Q: and u = then the distance from y to Span{u} = line through the origin and y is 2/10. Let y = True…

A:

Q: Evaluate F.dr where F(x, y) = xy i+ej and C is the line segment from (2, 0) to (4, 0). a) 0 b) 2 c)…

A: Consider the given information. Fx,y=xyi+exj and the line segment is from 2,0 to 4,0. Now, write the…

Q: 2 (720). 8 If the length of the curve y = 3 x, from the point (0, 0) to the point (xo, f(xo)) is L=…

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Q: nclosed between the curves y= r'and x= y? 18 16 14 12 12 14 16 18 -1 -1 O 02 04 0.8 0.6 0.4 0.2 0.6…

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Q: Find the length of the curve. 9. r(t) = i-j+ 6t k, 1sts3 %3D 74 3 88 3 O 16 3 O 70 3 92 3

A:

Q: Find the length of the curve 3y = (x² + 1) ? from x = 0 to x = 3.

A: Given:

Q: If y2 + xy = 1, find y" at the point (0, -1) %3D

A:

Q: X. xy ds where C is the straight line from (2,3) to (4,0).

A: Given: The curve C is the straight line from 2,3 to 4,0, To find: The value of ∫Cxy2ds.

Q: r(2,4) Sa (2y+x) dx +(3x– y)dy} along the straight line x-2t and Evaluate J(0,3) y=P+3.

A:

Q: S. 3 z dz where C is straight line segment from i to -2 - 3i

A: We put z=x+iy And dz=dx+idy

Q: Q2: Find the distance from the point R( 2,2,10) to the line: x=t y=1+t z = 3-t

A: Here first we select a general point on the line Now, we find the direction vector of that point to…

Q: I – 1 f(r) = I +1 f(x): that are parallel to the line x – – 2y = 2.

A:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.