   Chapter 11.3, Problem 45E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Write the equation of the line tangent to the curve x e y = 2 y + 3  at (3,0) .

To determine

To calculate: The equation of the tangent line to the curve xey=2y+3 at (3,0).

Explanation

Given Information:

The provided equation of the curve is, xey=2y+3 and the point is (3,0).

Formula used:

The slope of tangent to a curve y=f(x) at point (x,y) is given by the derivative of the curve at that point.

The equation of a line passing through points (x1,y1) and slope m is given by:

yy1=m(xx1)

Calculation:

Consider the provided equation of curve,

xey=2y+3

Now, find the derivative dydx from xey=2y+3 by taking the derivative term by term on both sides of the equation as,

ddx(xey)=ddx(2y)+ddx(3)xeydydx+ey=2dydx+0

Solve for dydx as,

xeydydx+ey=2dydx+0ey

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