Show that the statement limx→2(14−5x)=4 using the precise definition of a limit.
Based from the definition,
if 0<|x−a|<δ then |f(x)−L|<ε
if 0<|x−2|<δ then |(14−5x)−4|<ε
But,
|(14−5x)−4|=|14−5x−4|=|10−5x|=|−5(x−2)|=5|x−2|
So we want
if 0<|x−2|<δ then 5|x−2|<ε
That is,
if 0<|x−2|<δ then |x−2|<ε5
The statement suggest that we should choose δ=ε5.
By proving that the assumed value of δ=ε5 will fit the definition.
if 0<|x−2|<δ then,
|(14−5x)−4|=|14−5x−4|=|10−5x|=|−5(x−2)|=5|x−2|<5δ=\cancel5(ε\cancel5)=ε
Thus,
if 0<|x−2|<δ then |(14−5x)−4|<ε
Therefore, by the precise definition of a limit
limx→2(14−5x)=4
Saturday, May 26, 2018
Single Variable Calculus, Chapter 2, Review Exercises, Section Review Exercises, Problem 19
Subscribe to:
Post Comments (Atom)
Why is the fact that the Americans are helping the Russians important?
In the late author Tom Clancy’s first novel, The Hunt for Red October, the assistance rendered to the Russians by the United States is impor...
-
There are a plethora of rules that Jonas and the other citizens must follow. Again, page numbers will vary given the edition of the book tha...
-
The poem contrasts the nighttime, imaginative world of a child with his daytime, prosaic world. In the first stanza, the child, on going to ...
-
Robinson Crusoe, written by Daniel Defoe, is a novel. A novel is a genre defined as a long imaginative work of literature written in prose. ...
-
In the late author Tom Clancy’s first novel, The Hunt for Red October, the assistance rendered to the Russians by the United States is impor...
-
Lionel Wallace is the subject of most of "The Door in the Wall" by H.G. Wells. The narrator, Redmond, tells about Wallace's li...
-
"The Wife's Story" by Ursula Le Guin presents a compelling tale that is not what it initially seems. The reader begins the sto...
-
In Celie's tenth letter to God, she describes seeing her daughter in a store with a woman. She had not seen her daughter since the night...
No comments:
Post a Comment