Differential Geometry | Topology Answers

Let f be a smooth function. Calculate the curvature and the torsion of the curve that is the intersection of x = y and z = f(x).

Calculate T ; N; B; "\\kappa" ; "\\tau" of the curve x(t) = (t; t ² ; t ⁴) at the point (1; 1; 1).

for the curve x=a(3u-u³), y=3au², z=a(3u+u³) prove that k=t

Show that {𝑥} ⊆ ℝ is connected

Show that {𝑥} ⊆ ℝ is connected.

Find the angle nearest to the whole number between the surfaces x2+y2+z2=9 and z=x2+y2-3 at the point (2, -1, 2).

sketch the astroid in curves also calculate its tangent vector at each point .at which point is the tangent vector zero:

(i) γ(t) = (cos^2 t, sin^2 t)

(ii) γ(t) = (e^t, t^2)

use the Bisection method with 3 iterations to find solutions for f(x) = x ^ 3 + x - 4 on interval [1, 4] .

Vector A=2ti+tj-t^3k and B=sinti+costj evaluate

A..d/dt(A.B)

B..d/dt(A.A)

C..d/dt(A×B)

D..show that d/dt(A×A) is equal to zero.