Chapter 13.3, Problem 31E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

At what point does the curve have maximum curvature? What happens to the curvature as *x* ⟶ ∞?

**30.** *y* = ln *x*

**31.** *y* = *e ^{x}*

To determine

the point of curve
*x* tends to infinity.

Explanation

**Given data:**

Vector function is

**Formula used:**

Consider a vector function of the curve in the form of

Write the expression for curvature.

Here,

*x*,

The equation
*y* is a function of *x*. Hence consider

Write the vector function of curve.

Substitute
*y*,

Apply differentiation with respect to *x* on both sides of equation.

Apply differentiation with respect to *x* on both sides of equation.

Substitute

The point of maximum curvature of the curve occurs at value of *x*, when

Apply differentiation with respect to *x* on both sides of equation (3).

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