   Chapter 2.3, Problem 54E

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# (a) The curve y = x / ( 1 + x 2 ) is called a serpentine.Find an equation of the tangent line to this curve at the point ( 3 , 0.3 ) .(b) Illustrate part (a) by graphing the curve and the tangent line on the same screen.

To determine

(a)

To find:

An equation of the tangent line to this curve at the point (3, 0.3)

Explanation

To find an equation of tangent line, first find derivative of the given function and then substitute the given value of x; it gives the slope of the tangent line. Then use point-slope form and find equation of line.

Given:

y=x1+x2, and given point is (3, 0.3)

Calculation:

Using quotient rule,

dydx=1+x2ddxx-xddx(1+x2)1+x22=1+x21-x(2x)1+x22=1

To determine

(b)

To graph:

The curve and the tangent line.

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