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Q2 (a) Using the definition, prove the following limits. i) lim(7x – 4) = 10 ii) lim x→2 x – 4 4x x-2 -4 %3D

Q2 (a) Using the definition, prove the following limits. i) lim(7x – 4) = 10 ii) lim x→2 x – 4 4x x-2 -4 %3D

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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Q2 (a) Using the definition, prove the following limits. 4х i) x→2 ii) lim х-2 х — 4 lim(7x – 4) = 10 %3D (b) Evaluate the following limits. i) ii) (а3х — а2х — а* + 1) V2x + 22 – 4 lim x→-3 - lim x + 3 2x2 1 (c) State the Mean Value Theorem. i) Verify the Mean Value Theorem for the function h(x) = 4x3 – 8x2 + 7x – 2 in the %3D interval [2,5]. ii) Using the Mean Value Theorem, prove that for any two real numbers a and b, |cos a – cos b| < |la – bl.
Transcribed Image Text:Q2 (a) Using the definition, prove the following limits. 4х i) x→2 ii) lim х-2 х — 4 lim(7x – 4) = 10 %3D (b) Evaluate the following limits. i) ii) (а3х — а2х — а* + 1) V2x + 22 – 4 lim x→-3 - lim x + 3 2x2 1 (c) State the Mean Value Theorem. i) Verify the Mean Value Theorem for the function h(x) = 4x3 – 8x2 + 7x – 2 in the %3D interval [2,5]. ii) Using the Mean Value Theorem, prove that for any two real numbers a and b, |cos a – cos b| < |la – bl.
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