   Chapter 12.5, Problem 53E

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# Maximum Curvature In Exercises 49-54, (a) find the point on the curve at which the curvature is a maximum and (b) find the limit of the curvature as x → ∞ . y = ln x

(a)

To determine

To calculate: The point on the curve at which the curvature is maximum.

Explanation

Given:

The function is: y=lnx.

Formula used:

The formula of curvature.

k=|y|[1+(y)2]32

Calculation:

Consider the provided function: y=lnx

Differentiate the function with respect to x:

Then, y=1x and y=1x2.

Now, substitute these value in formula.

k=|1x2[1+1x2]32|=x(x2+1)32

Now, differentiate K with respect to x

(b)

To determine

To calculate: The limit of the curvature as x→∞.

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