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Little algebra fun: a³ + b³ (sum of cubes) and a³ - 6³ (difference of cubes) can be factorized using (a + b)(a²- ab + b²) and (a - b)(a² + ab + b²), respectively. (a) Use the appropriate factorization formula to derive the conjugate of a¹/3 - 6¹/3. Can you deduce the conjugate of a¹/3 + b¹/3? (b) Using your answer in (a) evaluate the limit below: lim x-0 1-√x² +1 x²

Little algebra fun: a³ + b³ (sum of cubes) and a³ - 6³ (difference of cubes) can be factorized using (a + b)(a²- ab + b²) and (a - b)(a² + ab + b²), respectively. (a) Use the appropriate factorization formula to derive the conjugate of a¹/3 - 6¹/3. Can you deduce the conjugate of a¹/3 + b¹/3? (b) Using your answer in (a) evaluate the limit below: lim x-0 1-√x² +1 x²

Calculus: Early Transcendentals
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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Solutions to Question 4 please
Question 4 Little algebra fun: a³ + b³ (sum of cubes) and a³ - 6³ (difference of cubes) can be factorized using (a + b)(a²- ab + b²) and (a - b)(a² + ab + b²), respectively. (a) Use the appropriate factorization formula to derive the conjugate of a¹/3-b¹/3. Can you deduce the conjugate of a¹/3 +6¹/3? (b) Using your answer in (a) evaluate the limit below: lim x->0 f(x) = 1- x² +1 x² Question 5 Find the value(s) (if any) of k such that lim f(x) exists Justify your answer. k²x² 18kx + 8 x² - 9kx - 7 , x ≤ 1 , x > 1
Transcribed Image Text:Question 4 Little algebra fun: a³ + b³ (sum of cubes) and a³ - 6³ (difference of cubes) can be factorized using (a + b)(a²- ab + b²) and (a - b)(a² + ab + b²), respectively. (a) Use the appropriate factorization formula to derive the conjugate of a¹/3-b¹/3. Can you deduce the conjugate of a¹/3 +6¹/3? (b) Using your answer in (a) evaluate the limit below: lim x->0 f(x) = 1- x² +1 x² Question 5 Find the value(s) (if any) of k such that lim f(x) exists Justify your answer. k²x² 18kx + 8 x² - 9kx - 7 , x ≤ 1 , x > 1
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