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(a) Determine whether each of the following functions is continuous at 2. Name any results or rules that you use. You may use the basic continuous functions listed in Theorem D51 from Unit D4. (i) f(x)= (ii) f(x)= (iii) f(x) = 2-3x+x², | x² – 3, x≤ 2, x > 2. (x - 2)² sin (x-2), 10. (sin(TI), T≤2, ²-4, x > 2. x 2, x = 2.

(a) Determine whether each of the following functions is continuous at 2. Name any results or rules that you use. You may use the basic continuous functions listed in Theorem D51 from Unit D4. (i) f(x)= (ii) f(x)= (iii) f(x) = 2-3x+x², | x² – 3, x≤ 2, x > 2. (x - 2)² sin (x-2), 10. (sin(TI), T≤2, ²-4, x > 2. x 2, x = 2.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Determine whether each of the following functions is continuous at 2. Name any results or rules that you use. You may use the basic continuous functions listed in Theorem D51 from Unit D4. (i) f(x) = (ii) f(x) = (iii) f(x) = 2-3x+x², x² - 3, .2 x≤ 2, x > 2. [(x - 2)² sin (2) 10, sin(x), x≤ 2, x² - 4, x > 2. x = 2, p is given by 2 3x²-3x+1. x = 2. (b) The polynomial p(x) = 3x³ (i) Determine a real number M such that p has no zeros outside the interval (-M, M), and exactly three zeros in (-M, M). (ii) Determine an open interval of length in R that contains exactly one zero of p.
Transcribed Image Text:(a) Determine whether each of the following functions is continuous at 2. Name any results or rules that you use. You may use the basic continuous functions listed in Theorem D51 from Unit D4. (i) f(x) = (ii) f(x) = (iii) f(x) = 2-3x+x², x² - 3, .2 x≤ 2, x > 2. [(x - 2)² sin (2) 10, sin(x), x≤ 2, x² - 4, x > 2. x = 2, p is given by 2 3x²-3x+1. x = 2. (b) The polynomial p(x) = 3x³ (i) Determine a real number M such that p has no zeros outside the interval (-M, M), and exactly three zeros in (-M, M). (ii) Determine an open interval of length in R that contains exactly one zero of p.
Theorem D51 Basic continuous functions The following functions are continuous: (a) polynomials and rational functions (b) f(x) = |x| (c) f(x)=√x (d) the trigonometric functions sine, cosine and tangent (e) the exponential function.
Transcribed Image Text:Theorem D51 Basic continuous functions The following functions are continuous: (a) polynomials and rational functions (b) f(x) = |x| (c) f(x)=√x (d) the trigonometric functions sine, cosine and tangent (e) the exponential function.
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