5. Prove or disprove: Let l', and I; be two simple graphs; with V(T)| = m, E(T)=p.V(T)| =n, E(T2)| = q. Then E(T, , r2 =p+q +mn

Q: a Show that y = mx + b intersects y = |x + 1| if m > 1 or m < -1. b Given that -1 < m < 1, find the…

A: Given,y = mx + cFor m &gt; 1Take  m = 2 &gt; 1,

Q: 6. Find the shortest distance from B6,0,0) to the pane Ax + By tCz +D= 0 where A, B,C and D SR .

A:

Q: 1.. The olation to y'tby'494=o is, 0)- The eolution to yl +94=5 G8wt will exhibits d) Jesononce when…

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

Q: |-*^= 39. What is the length of the curve y = √x- between x = 0 and x = 2?

A:

Q: Find the length of the curve over the given interval. r = 8, [0, π/6]

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: If the first line has the form Ax + By + C = 0 and the second line has the form Dx + Ey + F = 0 and…

A: The first line is of the form Ax+By+C=0and the second line is of the form Dx+Ey+F=0 As the first…

Q: Let C be the shortest path that connects n to ni and I = [, (sinhz + 1)dz. Then O I=-sinh n+ n(i-1)…

A: Second option is correct answer i . e . I = -1-cosh(π)+π(i-1)

Q: 2. Consider any five points P1, Ps in the interior of a square S of side length 1. Show that one can…

A: To solve this problem we use the Pigeonhole principle . Pigeonhole principle : If there are m holes…

Q: 2 32 |for 1st<3. length of the curve c(t) =| In t,-t"

A:

Q: Consider the accompanying graphs of y = 2x + 3 and y = In x. Determine the %3D a. minimum vertical…

A: (a) Given information:

Q: Q4) Compute f z'dz, where C is the path formed by the line segment from -3 to 3 and the semicircle…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: 8. What is the rate of change of the edge length s of a cube Vith respe ds С. ds D. dV 1 ds В. dv…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: . Consider the accompanying graphs of y = 2r + 3 and y = In x. Determine the a. minimum vertical…

A: Given, y=2x+3 and y=lnx. And, the graph is shown below: a. Let Ax,y=x1,2x1+3 and Bx,y=x1,lnx1 be…

Q: 8 (6562) 243 를-), then xo = If the length of the curve y = 3 x7 from the point (0, 0) to the point…

A:

Q: 1) Evaluate S,(x – y)dx + (y – z)dy + xdz where C is the curve from (1. –2, 3) to (–4, 5, 2) if a) C…

A: Given integral: ∫Cx-ydx+y-zdy+xdz Here, C is the curve from 1,-2,3 to -4,5,2 a) The parametric…

Q: Find the exact length af te of the curve, 2. x-

A:

Q: Find the length of the curve y = In(e - 1) – In(e + 1), In 2 sxsIn 3.

A:

Q: 1. Find the length of the curve: y = x/2 , x = 0 to x = 4

A:

Q: y = 4 1 ,2 In x, 1<x < 2 2 -

A:

Q: Find a path c(t) that traces the line y = 2x + 1 from (1, 3) to (3, 7) for 0 ≤ t ≤ 1.

A: Given:

Q: 8) Wihat is the length of the pot Df the curve y2=(x-1)between the points (4,0) ond (2,4) ?

A: Let f(x) be a smooth function over the interval [a,b]. Then the arc length of the portion of the…

Q: б. (a) Sketch the level curves z = k for k = 0, 1, 2 if z = x2 – y?.

A: The level curves of a function f of two variables are the curves with equations f(x, y) = c, where c…

Q: Re Question 17 Find a parameterization for the line segment from (2,-1) to (-6, 4). a) O (t) = -1–…

A:

Q: ==, j= 4 and x=0 about tue liney=5

A: Disk method: -  When the axis of revolution is the plane region's boundary and the cross-sectional…

Q: Find the length of the curve given by S(x) = (a -) defined on the interval (1, 2].

A: Consider the given curve:

Q: 1. Find the length of the curve y = x2 from x 1 to x = 4.

A: According to our guidelines, we can answer only the first question, the rest can be reposted.

Q: et y = [ 2   3   -1] and u = [ 2   -6   -6] compute the distance d from y to the line through u and…

A: first we shall find equation of line then find distance from line of that point

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: Find the exact length of the curve. y = In(1 - x²), o s x s

A: Solve the problem using definite integral

Q: 4. Evaluate S. y² – 3z + 2 ds for each of the following curve C is the line segment from (1,0,4) to…

A: We have ∫Cy2-3z+2 ds C is the line segment from 1,0,4 to 2,-1,1 Now, the parametric equation of the…

Q: The tangent to the circle x2 +y2 +10 x+5 y= 60 at the point (2 ,4) is Select one: O None O 13 y +…

A: Given that:x2+y2+10x+5y=60

Q: ii) Prove that the straight line y = x is the curve giving the shortest distance between the points…

A:

Q: graph

A:

Q: For what values of k does the family of curves =² + (y – c)² = kc² have an envelope?

A: Eliminate C from f and f'c

Q: 3/2 The length of the curve x= 4y2 from y=1 to y= 4 is given by

A:

Q: Find the total length of the loop of the curve 6y^2 = x (x - 2)^2 between x = 0 and x = 2.

A:

Q: (1) Give two different parameterizations for each of the following curves. (a) The line segment from…

A:

Q: If the fGD@ of the instantaveous rate of Chnange of (2,-6)isy tie tangent to bet x wriTre re ef…

A:

Q: | 6. Let y = 3 and u = . Compute the distance from y to the line through u 1 2 and the origin.

A: Given: y=-231  and u=1-12 To compute: the distance from y to the line through u and the origin.…

Q: 6 - Find the length of the curve y = (x)7 from the x = 0 to x = 4. a) O 8/27(10^(3/2)+2) b) O…

A: .

Q: Suppose that dy xy + x d.x and that the point (5,0) lies on the graph of (x, y). What is the value…

A:

Q: 1. Evaluate | (x- y)ds over the path C:r(t) = 4ti + 3tj for 0 <t<2.

A: Answer

Q: Find the length of the curve ƒ1x2= x3&gt;2 between x = 0 and x = 4 (as shown).

A: Given curve is fx=x32. To find the length of curve between x=0 and x=4. Solution: We know that…

Q: Find the length of the curve defined by y = 3 In 3 from x = 8 to x = 9.

A: Use derivative of function and length of curve formula .

Q: Find the exact length of the curve. y = 4 글2-글 In(x), 1 < x < 4

A:

Q: 3) Find the exact length of the curve y = x² – In x for 1< x < 2. 1„2

A:

Q: Use the TRAPEZOIDAL with 3 level Romberg (k = 3) to evaluate: e* sin x , 1+x²

A:

Q: Find the exact length of the curve. y = In(1 - x²), o sxs

A: Find dy/dx, then put it in the arc length formula.

Q: 4 The line y= -Lx+3 has a perpendicu lar which fangent to the graph of y= (x²-2) (2x+k) at x=-l,…

A:

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.