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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, x≤ 2, x² - 3, x > 2. (=-=-=-2) J (x. (x - 2)² sin x≤ 2, sin(x), ²-4, x>2. 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, x≤ 2, x² - 3, x > 2. (=-=-=-2) J (x. (x - 2)² sin x≤ 2, sin(x), ²-4, x>2. 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, x≤ 2, [x² - 3, x > 2. J (x. (x - 2)² sin X- sin(x), x≤ 2, ²-4, x>2. 2 x = 2, x = 2.
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, x≤ 2, [x² - 3, x > 2. J (x. (x - 2)² sin X- sin(x), x≤ 2, ²-4, x>2. 2 x = 2, x = 2.
We end this subsection with a reminder of the various approaches that you have met for investigating the continuity of a function f: A Rat a € A. Recall that you should first guess whether f is continuous or discontinuous at a, then check whether your guess is correct (a sketch of the graph may help you make your guess). You can check your guess using Strategy D14. You have also seen that, in many cases, it is possible to show that f is continuous at a by applying rules such as the Combination Rules, the Composition Rule, the Squeeze Rule and the Glue Rule to functions which you already know to be continuous. We have proved that a number of familiar functions are continuous and we now collect these together in the following result. 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:We end this subsection with a reminder of the various approaches that you have met for investigating the continuity of a function f: A Rat a € A. Recall that you should first guess whether f is continuous or discontinuous at a, then check whether your guess is correct (a sketch of the graph may help you make your guess). You can check your guess using Strategy D14. You have also seen that, in many cases, it is possible to show that f is continuous at a by applying rules such as the Combination Rules, the Composition Rule, the Squeeze Rule and the Glue Rule to functions which you already know to be continuous. We have proved that a number of familiar functions are continuous and we now collect these together in the following result. 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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