   Chapter 9, Problem 41RE Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

In Problems 40 and 41, decide whether the statements are true or false. lim h → 0 f ( c + h ) − f ( c ) h gives the equation of the tangent line to f ( x )  at  x   =   c .

To determine

Whether the provided statement, “limh0f(c+h)f(c)h gives the equation of tangent line to f(x) at x=c” is true or false.

Explanation

Consider the provided statement, “limh0f(c+h)f(c)h gives the equation of tangent line to f(x) at x=c”.

Consider the provided formula,

limh0f(c+h)f(c)h

The slope of the tangent is equal to the derivative of the equation of the surface, to which the line is tangent to.

The formula for derivative is

limh0f(x+h)f(x)h

Thus, the provided formula gives the slope of the tangent and not the equation of tangent

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