EvaluateRC F·dr where F = hyzexz,exz,xyexzi and C : r = ht2 + 1,t2 −1,t2 −2ti,...

EvaluateRC F·dr where F = hyzexz,exz,xyexzi and C : r = ht2 + 1,t2 −1,t2 −2ti, 0 ≤ t ≤ 2. Hint: Check whether F is conservative. If so, the Fundamental Theorem for Line Integrals might be useful

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milcah answered 2 years ago

3) Solve the initial value problems c) R′ + (R/t) = (2/(1+t2 )) , R(1) =...

3) Solve the initial value problems c) R′ + (R/t) = (2/(1+t2 )) , R(1) = ln 8. e) ) cos θv′ + v = 3 , v(π/2) = 1. 5) Express the general solution of the equation x ′ = 2tx + 1 in terms of the erf function. 7) Solve x ′′ + x ′ = 3t by substituting y = x ′ 9) Find the general solution to the differential equation x ′ = ax + b,...

1. Consider the function f: R→R, where R represents the set of all real numbers and...

1. Consider the function f: R→R, where R represents the set of all real numbers and for every x ϵ R, f(x) = x3. Which of the following statements is true? a. f is onto but not one-to-one. b. f is one-to-one but not onto. c. f is neither one-to-one nor onto. d. f is one-to-one and onto. 2. Consider the function g: Z→ {0, 1, 2, 3, 4, 5}, where Z represents the set of all integers and for...

Given the line integral ∫c F(r) · dr where F(x, y, z) = [mxy − z3...

Given the line integral ∫c F(r) · dr where F(x, y, z) = [mxy − z3 ,(m − 2)x2 ,(1 − m)xz2 ] (a) Find m such that the line integral is path independent; (b) Find a scalar function f such that F = grad f; (c) Find the work done in moving a particle from A : (1, 2, −3) to B : (1, −4, 2).

Let l:ax1+bx2 =c be a line where a^2+b^2 =1.Find the map f: R^2 →R^2 that represents...

Let l:ax1+bx2 =c be a line where a^2+b^2 =1.Find the map f: R^2 →R^2 that represents the reflection about l. Verify that the transformation f found in Problem 1 is an isometry.

Consider the following history H: T2:R(Y), T1:R(X), T3:R(Y), T2:R(X), T2:W(Y), T2:Commit, T1:W(X), T1:Commit, T3:R(X), T3:Commit Assume...

Consider the following history H: T2:R(Y), T1:R(X), T3:R(Y), T2:R(X), T2:W(Y), T2:Commit, T1:W(X), T1:Commit, T3:R(X), T3:Commit Assume that each transaction is consistent. Does the final database state satisfy all integrity constraints? Explain.

Find a function f such that F = ∇f and use it to compute R C...

Find a function f such that F = ∇f and use it to compute R C Fdr along curve C. • F = <x, y>, C is part of the parabola y = x ^ 2 from (−1, 1) to (3, 9). • F = <4xe ^ z, cos (y), 2x ^ 2e ^ z>, where C is parameterized by r (t) = <t, t ^ 2, t ^ 4>, 0 ≤ t ≤ 1.

Let A ⊆ R, let f : A → R be a function, and let c...

Let A ⊆ R, let f : A → R be a function, and let c be a limit point of A. Suppose that a student copied down the following definition of the limit of f at c: “we say that limx→c f(x) = L provided that, for all ε > 0, there exists a δ ≥ 0 such that if 0 < |x − c| < δ and x ∈ A, then |f(x) − L| < ε”. What was...

Q2. Given the line integral C F (r) · dr where F(x,y,z) = [mxy − z3,(m...

Q2. Given the line integral C F (r) · dr where F(x,y,z) = [mxy − z3,(m − 2)x2,(1 − m)xz2] ∫ (a) Find m such that the line integral is path independent; (b) Find a scalar function f such that F = grad f ; (c) Find the work done in moving a particle from A : (1, 2, −3) to B : (1, −4, 2).

5. (a) Let f : R \ {−1} → R, f(x) = x+1. Show that f...

5. (a) Let f : R \ {−1} → R, f(x) = x+1. Show that f is injective, but not surjective. (b) Suppose g : R\{−1} → R\{a} is a function such that g(x) = x−1, where a ∈ R. Determine x+1 a, show that g is bijective and determine its inverse function.

Let f: [0 1] → R be a function of the class c ^ 2 that...

Let f: [0 1] → R be a function of the class c ^ 2 that satisfies the differential equation f '' (x) = e^xf(x) for all x in (0,1). Show that if x0 is in (0,1) then f can not have a positive local maximum at x0 and can not have a negative local minimum at x0. If f (0) = f (1) = 0, prove that f = 0

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