/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 3 If limx鈫抍f(x)-f(c)x-c聽exists,... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Q. 3 (page 896)

If limx鈫�cf(x)-f(c)x-cexists, it equals the slope of the ______ _____ to the graph of f at the point c,fc.

Short Answer

Expert verified

If limx鈫�cf(x)-f(c)x-cexists, it equals the slope of thetangentlineto the graph offat the pointc,fc.

Step by step solution

01

Step 1. Given Information

The slope of the tangent line through a point on the graph of a function provides the function's instantaneous rate of change at that point.

02

Step 2. Filling the blank

As we know the tangent of a line to the graph of the function f(x)at the point c,f(c)has a slope of limx鈫�cf(x)-f(c)x-c.

So, if limx鈫�cf(x)-f(c)x-cexists, it equals the slope of the tangent line to the graph offat the pointc,f(c).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Problems 13鈥�32, use the accompanying graph of y = f(x).

Findlimx鈫�-4-f(x).

In Problems 7鈥� 42, find each limit algebraically

limx鈫�25x4

True or False Some rational functions have holes in their graph.

Graph each function. Use the graph to find the indicated limit, if it exists.

limx鈫�4f(x),f(x)=3x+1

In Problems 45-60, determine whether fis continuous at c.

f(x)=x3-3x2+2x-6,c=2
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.