   Chapter 2.7, Problem 8E

Chapter
Section
Textbook Problem

Find an equation of the tangent line to the curve at the given point. y = 2 x + 1 x + 2 ,   ( 1 , 1 )

To determine

To find: The equation of the tangent line to the curve at the given point.

Explanation

Given:

The equation of the curve is y=2x+1x+2.

The curve passing through the point (1, 1).

Formula used:

The slope of the tangent curve y=f(x) at the point P(a,f(a)) is,

m=limxaf(x)f(a)xa (1)

The equation of the tangent line to the curve y=f(x) at the point (a,f(a)) is,

yf(a)=f(a)(xa) (2)

Calculation:

Obtain the slope of the tangent line to the parabola at the point (1, 1).

Substitute a=1 and f(a)=1 in equation (1),

m=limx1f(x)f(1)x1=limx1(2x+1x+2)1x1=limx1(2x+1)1(x+2)(x+2)x1=limx1((2x+1)(x+2)(x1)(x+2))

=limx12x+1x2

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