Consider the cunc y1-x a) Find the curvature K of C at the point P(1, 0) b) Find the radius r of curvature of C at the point P(1, 0) c) Find the center of curvature of C at the point P(1, 0) d) Find the rectangular equation of the circle of curvature at the point P(1, 0) 3. Consider the curve C: y In(x). Find the point or points on C at which the curvature K is a maximum 4. Find the curvature K of the curve C: y f(x) = x -3x+2 at the point where f attains its relative maximum. at which the curvature is 0. 5. Find the point or points on the curve C: y e 6. Find the radius of curvature of the circular helix described by: r(t) cos (2t)i+ sin (2t) j+ tk at the point P-1, 0, of the twisted cubic with 7. Compute T, N, K, AT, AN at the point P 1, 2' 3 1.2 t, y=t, z =t3 with teR. parametric equations x 2

Question

Please solve all parts.

Consider the cunc y1-x
a) Find the curvature K of C at the point P(1, 0)
b) Find the radius r of curvature of C at the point P(1, 0)
c) Find the center of curvature of C at the point P(1, 0)
d) Find the rectangular equation of the circle of curvature at the point P(1, 0)
3. Consider the curve C: y In(x). Find the point or points on C at which the
curvature K is a maximum
4. Find the curvature K of the curve C: y f(x) = x -3x+2 at the point
where f attains its relative maximum.
at which the curvature is 0.
5. Find the point or points on the curve C: y e
6. Find the radius of curvature of the circular helix described by:
r(t) cos (2t)i+ sin (2t) j+ tk at the point P-1, 0,
of the twisted cubic with
7. Compute T, N, K, AT, AN at the point P 1,
2' 3
1.2
t, y=t, z =t3 with teR.
parametric equations x
2

Image Transcription

Consider the cunc y1-x a) Find the curvature K of C at the point P(1, 0) b) Find the radius r of curvature of C at the point P(1, 0) c) Find the center of curvature of C at the point P(1, 0) d) Find the rectangular equation of the circle of curvature at the point P(1, 0) 3. Consider the curve C: y In(x). Find the point or points on C at which the curvature K is a maximum 4. Find the curvature K of the curve C: y f(x) = x -3x+2 at the point where f attains its relative maximum. at which the curvature is 0. 5. Find the point or points on the curve C: y e 6. Find the radius of curvature of the circular helix described by: r(t) cos (2t)i+ sin (2t) j+ tk at the point P-1, 0, of the twisted cubic with 7. Compute T, N, K, AT, AN at the point P 1, 2' 3 1.2 t, y=t, z =t3 with teR. parametric equations x 2

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Derivative