Answer The limit of the function is − 0.75 Explanation Given information: Sketch a graph of the function and approximate the limit (if it exists). Then find the limit (if it exists) algebraically by using appropriate technique(s). lim x → − 2 x 2 − 1 2 x Calculation: Consider the given function, lim x → − 2 x 2 − 1 2 x Sketch a graph of the function use graphing utility T I − 83 Press Y and key and observe the screen, Now press WINDOW to choose proper scale, Now press GRAPH and display will be, Now verify the existence of limit, Press 2 n d window and display will be. Now enter the values of X as X = 1.9 , 1.99 , 2 , 2.001 , 2.01 , 2.1 and ENTER successively. As the value of the function approaches to the same value as X approaches from left and right the limit at x = − 2 exists. Now evaluate the limit of function by substitution x = − 2 by direct substitute method. lim x → − 2 x 2 − 1 2 x = ( − 2 ) 2 − 1 2 ( − 2 ) = 4 − 1 − 4 = − 3 4 = − 0.75 Hence the limit of the function is − 0.75

3rd Edition

ISBN: 9781285607160

Author: Larson

Publisher: CENGAGE CO

See similar textbooks

Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

Videos

Question

Chapter 12, Problem 1CT

To determine

Find the limit algebraically.

Expert Solution & Answer

Answer to Problem 1CT

The limit of the function is $−0.75$

Explanation of Solution

Given information:

Sketch a graph of the function and approximate the limit (if it exists). Then find the limit (if it exists) algebraically by using appropriate technique(s).

$limx→−2x2−12x$

Calculation:

Consider the given function,

$limx→−2x2−12x$

Sketch a graph of the function use graphing utility $TI−83$

Press Y and key and observe the screen,

EBK PRECALCULUS W/LIMITS, Chapter 12, Problem 1CT , additional homework tip 1

Now press WINDOW to choose proper scale,

EBK PRECALCULUS W/LIMITS, Chapter 12, Problem 1CT , additional homework tip 2

Now press GRAPH and display will be,

EBK PRECALCULUS W/LIMITS, Chapter 12, Problem 1CT , additional homework tip 3

Now verify the existence of limit, Press 2ⁿ^d window and display will be.

EBK PRECALCULUS W/LIMITS, Chapter 12, Problem 1CT , additional homework tip 4

Now enter the values of $X$ as $X=1.9,1.99,2,2.001,2.01,2.1$ and ENTER successively.

EBK PRECALCULUS W/LIMITS, Chapter 12, Problem 1CT , additional homework tip 5

As the value of the function approaches to the same value as $X$ approaches from left and right the limit at $x=−2$ exists.

Now evaluate the limit of function by substitution $x=−2$ by direct substitute method.

$limx→−2x2−12x=(−2)2−12(−2)=4−1−4=−34=−0.75$

Hence the limit of the function is $−0.75$

Chapter 12, Problem 108RE

Chapter 12, Problem 2CT

Chapter 12 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - Prob. 7E Ch. 12.1 - Prob. 8E Ch. 12.1 - Prob. 9E Ch. 12.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.