Q. 47 find the limit as x approaches c... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 14: Q. 47 (page 883)

find the limit as x approaches c of the average rate of change of each function from c to x.
$c = - 1; f (x) = x^{2} + 2 x$

Short Answer

Expert verified

Limit is $0$

Step by step solution

Given information is

$c = - 1; f (x) = x^{2} + 2 x$

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

$\frac{鈭� y}{鈭� x} = \frac{f (x) - f (c)}{x - c} \frac{鈭� y}{鈭� x} = \frac{x^{2} + 2 x - (c^{2} + 2 c)}{x - c} \frac{鈭� y}{鈭� x} = \frac{x^{2} + 2 x - ({(- 1)}^{2} + 2 (- 1))}{x + 1} \frac{鈭� y}{鈭� x} = \frac{x^{2} + 2 x - (1 - 2)}{x + 1} \frac{鈭� y}{鈭� x} = \frac{x^{2} + 2 x + 1}{x + 1}$

Step 3. Solving we get,

$\frac{鈭� y}{鈭� x} = \frac{x^{2} + 2 x + 1}{x + 1} \frac{鈭� y}{鈭� x} = \frac{{(x)}^{2} + 2 脳 1 脳 x + 1^{2}}{x + 1} \frac{鈭� y}{鈭� x} = \frac{{(x + 1)}^{2}}{x + 1} \frac{鈭� y}{鈭� x} = (x + 1)$

Step 4. Finding the limit we get,

$\lim_{x 鈫� c} \frac{鈭� y}{鈭� x} = \lim_{x 鈫� c} \frac{f (x) - f (c)}{x - c} \lim_{x 鈫� - 1} \frac{鈭� y}{鈭� x} = \lim_{x 鈫� - 1} (x + 1) \lim_{x 鈫� c} \frac{鈭� y}{鈭� x} = - 1 + 1 \lim_{x 鈫� c} \frac{鈭� y}{鈭� x} = 0$

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91影视

find the limit as x approaches c of the average rate of change of each function from c to x.
$c = - 1; f (x) = x^{2} + 2 x$

Short Answer

Step by step solution

Given information is

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

Step 3. Solving we get,

Step 4. Finding the limit we get,

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91影视

find the limit as x approaches c of the average rate of change of each function from c to x.c=-1;f(x)=x2+2x

Short Answer

Step by step solution

Given information is

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

Step 3. Solving we get,

Step 4. Finding the limit we get,

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Discrete Mathematics

Geometry

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

find the limit as x approaches c of the average rate of change of each function from c to x.
$c = - 1; f (x) = x^{2} + 2 x$