4. Assume that the curvature of a path described by the vector-valued function r(t) can be ||r' (t) x r" (t) || expressed by the formula Show that the curvature of a curve y = ||r' (t)||3 the xy-plane can be found using the formula f(x) in |f" (x)| √√1+|f'(x)|2³

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A:

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A: Directional derivative of the function

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Q: Use the formula (x) K(X) = = y = 3x4 = |f"(x)| [1 + (F'(x))²] ³ 3/2 to find the curvature.

A: y=3x4

Q: 6. Where does the tangent line to r = at the point (1, 0, 1) intersect the y-z plane.

A: Given:

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A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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A:

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A:

Q: Pind the curvature x of the curve given by 7(()- (V2)i+ (e)j+(e)k, at the point P(0, 1, 1),

A: Curvature K = |r' x r"|/|r'|^3

Q: Use the formula x(x) = = K(x) = y = 3x4 |f"(x)| [1 + (²²(x))²] ¹ to find the curvature.

A: Given information:Function: To find:The curvature of the function .Concept used:The curvature of a…

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A: To find The curvature of the space curve

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A: Given α(t)=(t,t22,t36)

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A: First we will plot the given parameters.

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A: we will find the required solution.

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