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Consider the cunc y1-xa) 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 thecurvature K is a maximum4. Find the curvature K of the curve C: y f(x) = x -3x+2 at the pointwhere f attains its relative maximum.at which the curvature is 0.5. Find the point or points on the curve C: y e6. 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 with7. Compute T, N, K, AT, AN at the point P 1,2' 31.2t, y=t, z =t3 with teR.parametric equations x2

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
help_outline

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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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Step 1

You have asked multiple unrelated questions in a single post. Futher your first question has multiple sub parts. I will address all the sub parts of the first question. Please post balance questions one by one separately.

Step 2

Part (a)

Given curve:

y = 1 – x2

Recall the famous rule of differentiation: d(xn) / dx = nxn-1

Hence, y’ = -2x

Hence, y’ at P (1, 0) = -2 x 1 = -2

y’’ = -2

Step 3

Please see the white board for the formula ...

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Tagged in

Math

Calculus

Derivative

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