Explanation Given information: The parabola function is, y = e x , − 1 ≤ x ≤ 2 (1) Formula used: Write a general expression to calculate the maximum curvature. κ ( x ) = | f ″ ( x ) | [ 1 + ( f ′ ( x ) ) 2 ] 3 2 (2) Here, f ′ ( x ) is the first order derivative, and f ″ ( x ) is second order derivative. Calculation: From the given data, f ( x ) = y Substitute y for f ( x ) in equation (2) to find κ ( x ) . κ ( x ) = | y ″ | [ 1 + y ′ 2 ] 3 2 (3) Take first order derivative for equation (1) to find y ′ . y ′ = e x ( 1 ) = e x Take a derivative for above equation to find y ″ . y ″ = e x ( 1 ) = e x Substitute e x for y ″ , e x for y ′ in equation (3) to find κ ( x ) . κ ( x ) = | e x | [ 1 + ( e x ) 2 ] 3 2 κ ( x ) = e x [ 1 + e 2 x ] 3 2 (4) Substitute 0 for x in equation (1) to find y ( 0 )

Thomas' Calculus Format: Unbound (saleable) With Access Card

14th Edition

ISBN: 9780134768762

Author: Hass, Joel R.^heil, Christopher D.^weir, Maurice D.

Publisher: Prentice Hall

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Chapter 13.4, Problem 26E

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Find the curvature of the given function then sketch the graph for f(x) and κ(x) together.

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Chapter 13.4, Problem 25E

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Chapter 13 Solutions

Thomas' Calculus Format: Unbound (saleable) With Access Card

Ch. 13.1 - In Exercises 1–4, find the given limits. 1. Ch. 13.1 - In Exercises 1–4, find the given limits. 2. Ch. 13.1 - In Exercises 1–4, find the given limits. 3. Ch. 13.1 - In Exercises 1–4, find the given limits. 4. Ch. 13.1 - Motion in the Plane In Exercises 5–8, r(t) is the...Ch. 13.1 - Motion in the Plane In Exercises 5–8, r(t) is the...Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

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Find the curvature of the given function then sketch the graph for f ( x ) and κ ( x ) together.

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Find the curvature of the given function then sketch the graph for f(x) and κ(x) together.

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Chapter 13 Solutions