   Chapter 13.3, Problem 29E

Chapter
Section
Textbook Problem

# Use Formula 11 to find the curvature.27. y = x428. y = tan x29. y = xex

To determine

To find: The curvature of y=xex using Formula 11.

Explanation

Given data:

Plane equation is y=xex .

Formula used:

Consider a plane curve equation in the form of y=f(x) .

Write the expression for curvature according to Formula 11.

k(x)=|f(x)|[1+(f(x))2]32 (1)

Here,

f(x) is function of x,

f(x) is first derivative of function f(x) , and

f(x) is second derivative of function f(x) .

The equation y=xex indicates y is a function of x. Hence consider y=f(x) .

Write the plane equation.

y=xex

Substitute f(x) for y,

f(x)=xex

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

f(x)=ddx(xex)=xddx(ex)+ddx(x)ex {ddt(uv)=uv+uv}=x(ex)+(1)ex {ddt(et)=et,ddt(t)=1}=ex(1+x)

Apply differentiation with respect to x on both sides of equation

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