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The limit, lim 2(x + h) ² - 2x² h-0 h

The limit, lim 2(x + h) ² - 2x² h-0 h

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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The limit, lim h→0 2(x + h)² - 2x² h lim h→0 2(x +h)² - 2x² h To find this limit, the FOIL method can be used to expand the expression in the numerator. Then, simplify the numerator; distribute to remove the parentheses and combine like terms. = = = lim h→0 lim h→0 7 lim h→0 has the indeterminate form 2(x2 + 2x² + 4xh + h h 0 at h = 0 and h is a common factor of the numerator and denominator. 0 h h²) - : 2x² xh xh + 2h² - 2x² We cannot let h→0 until the factor h is removed from the denominator. Notice that the two remaining terms in the numerator of the result have a common factor of h.
Transcribed Image Text:The limit, lim h→0 2(x + h)² - 2x² h lim h→0 2(x +h)² - 2x² h To find this limit, the FOIL method can be used to expand the expression in the numerator. Then, simplify the numerator; distribute to remove the parentheses and combine like terms. = = = lim h→0 lim h→0 7 lim h→0 has the indeterminate form 2(x2 + 2x² + 4xh + h h 0 at h = 0 and h is a common factor of the numerator and denominator. 0 h h²) - : 2x² xh xh + 2h² - 2x² We cannot let h→0 until the factor h is removed from the denominator. Notice that the two remaining terms in the numerator of the result have a common factor of h.
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