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Chapter 14: Q. 46 (page 883)

find the limit as x approaches c of the average rate of change of each function from c to x.

c=3;f(x)=x3

Short Answer

Expert verified

Limit is9

Step by step solution

01

Step 1. Given information is

c=3;f(x)=x3

02

Step 2. An average rate change of function f  from point c to x

鈭�y鈭�x=f(x)-f(c)x-c鈭�y鈭�x=x3-c3x-c鈭�y鈭�x=(x-3)(x2-3x+32)x-3鈭�y鈭�x=(x2-3x+32)1=x2-3x+9

03

Step 3. Now, finding the limit we get,

limx鈫�c鈭�y鈭�x=limx鈫�cf(x)-f(c)x-climx鈫�c鈭�y鈭�x=limx鈫�3(x2-3x+9)limx鈫�c鈭�y鈭�x=(3)2-3(3)+9limx鈫�c鈭�y鈭�x=9-9+9limx鈫�c鈭�y鈭�x=9

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Most popular questions from this chapter

Use a graphing utility to find the indicated limit rounded to two decimal places.

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True or False The limit of a rational function at5 equals the value of the rational function at5

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