Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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My question is, for this question why do we skip the +x^n-3*a^2 part of the factorization formula?
Transcribed Image Text:1/26/2021
Section 2.3 Homework-Jessica Clements
Student: Jessica Clements
Date: 01/26/21
Instructor: Lori Green
Course: MTH-140 S21
Assignment: Section 2.3 Homework
Calculate the following limit using the factorization formula
x" -a"= (x-a)(x-1+x*
"-2a+x-3a? + .. + xa
-3 2
where n is a positive integer and a is a real number.
4
x-2401
lim
X-7
X-7
4
X -2401
Note that in this case,
is not defined at x = 7. Rewrite the function in the limit by factoring the numerator and
X-7
canceling common factors in the numerator and denominator before evaluating the limit.
Use the given factorization formula to factor the numerator and cancel like factors. Find the values of n and a in the given
rational functìon using the factorization formula x
^ -a" = (x-a)(x-1 +x'
n-2
a+x'
n-3 2
a +...+ Xa
n- 2
+a"-1).
%3D
4
In the polynomial x"-2401,n=4 and a = 7.
7x°+49x
3.
Substitute 4 for n and 7 for a into the factorization formula and simplify.
x* - 2401 = (x- 7)(x*-1 + x* -2(7) + x (7-2) +74-1)
= (x- 7)(x³ + 7x² +49x+ 343)
%3D
Now simplify the rational function.
4
X-2401
(x-7)(x° +7x² + 49x+ 343)
2
%3D
X-7
X-7
= x° +7x + 49x+343
4
X -2401
3
Finally, find lim
by evaluating lim (x°+7x+49x+ 343). Apply the limit law for polynomials shown below to
X-7
X→7
X→7
calculate the limit.
Assuming p is a polynomial and a is a constant, lim p(x)= p(a).
Xa
Substitute 7 for a and simplify.
lim (x³ + 7x2 + 49x+343) = 73+ 7 (72) + 49(7) +343
%3D
X-7
= 1372
4
X-2401
Therefore, lim
= 1372.
X-7
X-7
s ta
w
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