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.

Solutions

Expert Solution

milcah answered 1 year ago

Next > < Previous

Related Solutions

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...

Solve the problem. Let C(x) be the cost function and R(x) the revenue function. Compute the...

Solve the problem. Let C(x) be the cost function and R(x) the revenue function. Compute the marginal cost, marginal revenue, and the marginal profit functions. C(x) = 0.0004x3 - 0.036x2 + 200x + 30,000 R(x) = 350x Select one: A. C'(x) = 0.0012x2 - 0.072x + 200 R'(x) = 350 P'(x) = 0.0012x2 - 0.072x - 150 B. C'(x) = 0.0012x2 + 0.072x + 200 R'(x) = 350 P'(x) = 0.0012x2 + 0.072x + 150 C. C'(x) = 0.0012x2 -...

A probability density function on R is a function f :R -> R satisfying (i) f(x)≥0...

A probability density function on R is a function f :R -> R satisfying (i) f(x)≥0 or all x e R and (ii) \int_(-\infty )^(\infty ) f(x)dx = 1. For which value(s) of k e R is the function f(x)= e^(-x^(2))\root(3)(k^(5)) a probability density function? Explain.

Let f : R → R be a function. (a) Prove that f is continuous on...

Let f : R → R be a function. (a) Prove that f is continuous on R if and only if, for every open set U ⊆ R, the preimage f −1 (U) = {x ∈ R : f(x) ∈ U} is open. (b) Use part (a) to prove that if f is continuous on R, its zero set Z(f) = {x ∈ R : f(x) = 0} is closed.

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

Use DeMorgan's law and Involution law to find the complement of the following function: f(A,B,C,D) =...

Use DeMorgan's law and Involution law to find the complement of the following function: f(A,B,C,D) = [A+(BCD) ' ] [ (AD) ' + B (C ' + A) ]

6. (a) let f : R → R be a function defined by f(x) = x...

6. (a) let f : R → R be a function defined by f(x) = x + 4 if x ≤ 1 ax + b if 1 < x ≤ 3 3x x 8 if x > 3 Find the values of a and b that makes f(x) continuous on R. [10 marks] (b) Find the derivative of f(x) = tann 1 1 ∞x 1 + x . [15 marks] (c) Find f 0 (x) using logarithmic differentiation, where f(x)...

Suppose a function f : R → R is continuous with f(0) = 1. Show that...

Suppose a function f : R → R is continuous with f(0) = 1. Show that if there is a positive number x0 for which f(x0) = 0, then there is a smallest positive number p for which f(p) = 0. (Hint: Consider the set {x | x > 0, f(x) = 0}.)

Please Consider the function f : R -> R given by f(x, y) = (2 -...

Please Consider the function f : R -> R given by f(x, y) = (2 - y, 2 - x). (a) Prove that f is an isometry. (b) Draw the triangle with vertices A = (1, 2), B = (3, 1), C = (3, 2), and the triangle with vertices f(A), f(B), f(C). (c) Is f a rotation, a translation, or a glide reflection? Explain your answer.

Find a, b, c, and d such that the cubic function f(x) = ax3 + bx2...

Find a, b, c, and d such that the cubic function f(x) = ax3 + bx2 + cx + d satisfies the given conditions. Relative maximum: (3, 21) Relative minimum: (5, 19) Inflection point: (4, 20)

Subjects