2. Let C be the path given by a smooth vector valued function r(t) = S(0)i + g(t)j + h(t)k, astsb be a where a, b are non-negative constants. Let k(x, y, 2) be a continuous scalar funetion defined over R. Use this information to answer the following questions. a) Consider the path C :r(1) = r(21), SIs is it always the case that Justify your answer. b) Consider the path Ca i ni(t) = r("), Vasis vo, is it always the case that K(r, M. =) ds = k(1, W. =) ds? Justify your answer.

Q: #1. A function, F: R × R →R × R has been defined as follows: F(x, y) = (3y – 1, 1 - x) for all (x,…

A:

Q: The function f(x) has the following properties at x,: Af = 0.23751 and 0.24369, where h=0.1. Find…

A:

Q: 4y" – 8y' + 3y = 0

A: Given differential equation is 4y'' - 8y' + 3y = 0

Q: Let [1 M = 4 2 -3 be a vector in the vector space V of 2 × 2 matrices with real number entries. Let…

A:

Q: Find the solution. dy +y%3= dx 1 1+e* (A y = ce*+e*In (1+e*) B y = ce¯ - e-*In(1-e*) (c) y = ce-…

A:

Q: D.A.V. School of Delhi decided different types of tours for the students to educate them. So, in…

A:

Q: d"F (t) = (-t) f(t), where f=£{F}. Use this equation to compute £'(F}. One property of Laplace…

A: Given- One property of Laplace transforms can be expressed in terms of the inverse Laplace transform…

Q: a) In how many different ways can the letters of the word "CORPORATION" be arranged so that the…

A: Since you have posted a multiple  question according to guildlines I will solve first(Q(a))…

Q: the vectors are independent, enter zero in every answer blank since zer e equation below true. If…

A: Introduction: A set of vectors S=s1, s2, s3 is known as a linearly independent set of vectors if,…

Q: Question 2. The Fourier series representation, FS(t), of a periodic function of period 4 s given by…

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…

Q: What is the characteristic polynomial for the recurrence relation an = 5an-1 –7.2 (1) (x + 5)(x – 1)…

A: Given recurrence relation an=5an-1-7

Q: Solve the initial value problem with y(0) = 0 and y′(0) = 1. y′′ − y = cos(x)

A: To Solve the initial value problem with y(0) = 0 and y′(0) = 1.   y′′ − y = cos(x)

Q: Solve the initial value problem y" – y = cos(x) with y(0) = 0 and y (0) = 1.

A: Given differential equation is y'' - y = cos(x) with y(0) = 0  and  y'(0) = 1

Q: #3. Solve the fallowing Caucly problem in R" x(0,0) U4-Ou t cu = 0 u =9 On IR"x{t =0}. where c is a…

A: Given the Cauchy problem as  ut-∆u+cu=0,       in ℝn×0,∞           (1) re-write the equation (1) in…

Q: 0 1 2 3 4 5 6 7 8 9. Is the line of best fit accurate for the data shown? because the line does not…

A: A lines is said to be best fit if average point values are on the lines or closed to the line.

Q: The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the…

A: The given equations are x1'=6x1+6x2+5x3, x2'=-2x1-2x2-6x3 and x3'=2x1+2x2+6x3. The characteristic…

Q: Q.1 2 - A- 4 B= 5 Findd the following (chease 5 Only) A+ B 2.

A:

Q: Suppose p and q are distinct primes such that ordp a = h and ordq a = k Prove that ordpq a= lcm(h,…

A: Here we use basic group theory.

Q: 3 the sum of three conseutive numbers is 72 what is the smallest of these number? a 13

A: Introduction: Conditional statement is very significant in mathematics. A conditional statement is…

Q: Find the solution. y' = 5y + e-2x y-2, y(0) = 2 -15x 13e A) y = + 3e 2r1/3 23 139e 15x – 3e -2x \1/3…

A: Given differential equation is in the form of Bernoulli's differential equation.

Q: 5. Use rules of inference to show that the hypotheses "Joe works hard," "If Joe works hard, then he…

A: Given the hypotheses "Joe works hard" If Joe work hard ,then he is a dull boy If Joe is a dull boy…

Q: Prove that (R x Q) N (Q × R) = Q x Q

A:

Q: if z +0 f (z) = x²+y² 0, if z = 0.

A: The given problem is to show that the given complex function satisfies the CR equations at origin…

Q: Consider the given differential equation: y" – y" – 2y = 0. A) Show that the functions y1 = e¯*, y2…

A: We have to find the solution for the given problem.

Q: GIVE AN EQUATION OF THE PLANE DESCRIBED BELOW (A. ) containing (-5, 2, 4) and perpendicular to the…

A:

Q: Let f(x) = Vx. Use the definition of derivatives as limit of difference quotient to show that f'(x)…

A:

Q: find work done Let F G) and letc be unit circle centered on(2,0) note:r not constant

A:

Q: 11. 4, 8, 12, 16, 20

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Prove that an angle of θ radians is constructible if and only if the real number cosθ(sinθ)…

A: Since θ is constructible, by definition, (cosθ, sinθ) is a constructible point.

Q: The left-hand rule state that the user thumbs represent the X-axis and the .index represent the…

A: The left hand rule is that the thumbs represent the x-axis and the index represent the y-axis. Hence…

Q: Q2/ Defined x as 100 linearly spaced values between -2n to 2n. Defined y1 and y2 as sine and cosine…

A: To define x as 100 linearly spaced values between -2π to 2π . And define y1 and y2 .

Q: Solve the following maximization/minimization problems (a) max log(x,) + log(x2) subject to x1 + 3x,…

A:

Q: 3 Are the vectors -4 1 and linearly independent? -6 -8 -3 3 4 linearly dependent If they are…

A:

Q: 2. Find the general solutions of the following differential equations. y In y x InxX, y > 0 (b) (sin…

A:

Q: 5 -4t 2t

A:

Q: Evaluate the line integral by the two following methods. dx + x2 dy Cis counterclockwise around the…

A: The solution is given in the next steps.

Q: Sketch and identify the graph of the equation x² + y² – 2y – 3 = 0 in 3D.

A:

Q: Find the net area and the area of the region bounded by y = 11 cos x and the x-axis between x= - and…

A: The given problem is to find the net area and total area of the region bounded by given curves…

Q: Suppose that f (x) = x·g(x) for some function g that is continuous at 0. Prove that f is…

A:

Q: Construct proofs to show that the following symbolic arguments are valid.  Commas mark the breaks…

A:

Q: By volume, one alloy is %60 copper, %30 zinc, and %10 nickel. A second alloy has percents of %50,…

A: Introduction: A system of linear equations consists of more than one linear equation having more…

Q: Find the net area and the area of the region bounded by y = 11 cos x and the x-axis between x= - and…

A:

Q: b) A particle moves in simple harmonic motion according to the equation, s = 0 x Acos(wt)+ 0 ×…

A:

Q: Consider the decreasing sequence of functions {fn} defined on R, where fn(r) = X[n,00), Vn e N. That…

A:

Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | 8y dx…

A: Introduction: Green's theorem is one of calculus' four fundamental theorems, all of which are…

Q: Show that the centre of a ring R is a sub ring of R. And also show that the centre of a division…

A:

Q: The cyclic group of order 12 acts on {1,2,..., 12} with the following cycle structure. (1)…

A: Given that,  the group of order 12 In this case of necklace, there is no difference between…

Q: Use a fixed-point iteration method to determine a solution accurate to within 10-4 for x = tan x,…

A:

Q: Find the exact value of sin 0+ cos 0 if cos 0- 23 sin 0=13 and 180° <0<270°. ... sin 0+ cos 0 =…

A:

Q: (a) Find the coordinate vector of a = with respect to the ordered basis 4 E = of R³: [r]E = (b) Let…

A: