Question

Let γ : [c, d] −→ R 3 be a C 1 path and φ :...

Let γ : [c, d] −→ R 3 be a C 1 path and φ : [a, b] −→ [c, d] be a C 1 one-to one and onto map. Show that γ and γ ◦ φ have the same arclength. [Note that there are two cases depending on whether φ is orientation preserving or reversing.]

Homework Answers

Answer #1

the orientation preserving mean ist derivative is positive and reversing means its derivative is negative so i have that two cases

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1. Let D ⊂ C be an open set and let γ be a circle contained...
1. Let D ⊂ C be an open set and let γ be a circle contained in D. Suppose f is holomorphic on D except possibly at a point z0 inside γ. Prove that if f is bounded near z0, then f(z)dz = 0. γ 2. The function f(z) = e1/z has an essential singularity at z = 0. Verify the truth of Picard’s great theorem for f. In other words, show that for any w ∈ C (with possibly...
Let a, b, c, d be real numbers with a < b and c < d....
Let a, b, c, d be real numbers with a < b and c < d. (a) Show that there is a one to one and onto function from the interval (a, b) to the interval (c, d). (b) Show that there is a one to one and onto function from the interval (a, b] to the interval (c, d]. (c) Show that there is a one to one and onto function from the interval (a, b) to R.
Let 0 <  γ  <  α . Then a 100(1 −  α )% CI for μ...
Let 0 <  γ  <  α . Then a 100(1 −  α )% CI for μ when n is large is Xbar+/-zγ*(s/sqrt(n))The choice γ = α /2 yields the usual interval derived in Section 8.2; if γ ≠ α /2, this confidence interval is not symmetric about . The width of the interval is W=s(zγ+ zα-γ)/sqrt(n). Show that w is minimized for the choice γ = α /2, so that the symmetric interval is the shortest. [ Hints : (a)...
(1 point) Evaluate the line integral ∫F⋅d r∫CF⋅d r where F=〈-5sinx,-2cosy,10xz〉 and C is the path...
(1 point) Evaluate the line integral ∫F⋅d r∫CF⋅d r where F=〈-5sinx,-2cosy,10xz〉 and C is the path given by r(t)=(2t^3,-3t^2,-2t) for 0≤t≤10≤t≤1 ∫F⋅d r=
1. Let the angles of a triangle be α, β, and γ, with opposite sides of...
1. Let the angles of a triangle be α, β, and γ, with opposite sides of length a, b, and c, respectively. Use the Law of Cosines and the Law of Sines to find the remaining parts of the triangle. (Round your answers to one decimal place.) α = 105°;  b = 3;  c = 10 a= β= ____ ° γ= ____ ° 2. Let the angles of a triangle be α, β, and γ, with opposite sides of length a, b,...
Evaluate the line integral ∫F⋅d r∫CF⋅d r where F=〈sinx,−3cosy,5xz〉 and C is the path given by...
Evaluate the line integral ∫F⋅d r∫CF⋅d r where F=〈sinx,−3cosy,5xz〉 and C is the path given by r(t)=(-2t^3,-3t^2,3t) for 0≤t≤1
3 Let A = [0, 1) and B = (0, 1). Give an example to a...
3 Let A = [0, 1) and B = (0, 1). Give an example to a function f : A → B that is a) not one to one and not onto b) onto but not one to one c) one to one but not onto d*) one to one and onto
1. Let S and R be two relations below. R = {(1, 3), (1, 2), (8,...
1. Let S and R be two relations below. R = {(1, 3), (1, 2), (8, 0), (6, 9)} S = {(7, 5), (1, 6), (3, 1), (0, 3), (9, 4), (8, 6)} Please find S◦R and R◦S. Given two relations S and R on Z below, please determine the following relations. R = {(a, b) |a + 2 = b} S = {(a, b) |3a > b} (a) R−1 (b) R (c) R◦R (d) R−1 ◦ R (e) R−1...
Let A = {1, 2, 3, 4, 5, 6}. In each of the following, give an...
Let A = {1, 2, 3, 4, 5, 6}. In each of the following, give an example of a function f: A -> A with the indicated properties, or explain why no such function exists. (a) f is bijective, but is not the identity function f(x) = x. (b) f is neither one-to-one nor onto. (c) f is one-to-one, but not onto. (d) f is onto, but not one-to-one.
a) Let f : [a, b] −→ R and g : [a, b] −→ R be...
a) Let f : [a, b] −→ R and g : [a, b] −→ R be differentiable. Then f and g differ by a constant if and only if f ' (x) = g ' (x) for all x ∈ [a, b]. b) For c > 0, prove that the following equation does not have two solutions. x3− 3x + c = 0, 0 < x < 1 c) Let f : [a, b] → R be a differentiable function...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT