Recall that we say that lim f (x) = L if the (output) values, f(x), of ƒ get arbitrarily close to L as its input values approach a. “Arbitrarily close" means "as close as anyone might ever mandate", very loosely speaking. Please label the following statements as being true or false. Make sure you support your answer with a sketch. (a) If a is not in the domain of f , then lim f(x) is undefined. (b) If lim f() = 0 and lim f(x) = 3, lim f (x) might still be defined. x-a+ (c) If lim f(x) = f(a), then the graph of y = f (x) is continuous at x = a. %3D

Question
Recall that we say that lim f (x)
= L if the (output) values, f(x), of ƒ get arbitrarily close
to L as its input values approach a. “Arbitrarily close" means "as close as anyone might ever
mandate", very loosely speaking. Please label the following statements as being true or false.
Make sure you support your answer with a sketch.
(a) If a is not in the domain of f , then lim f(x) is undefined.
(b) If lim f() = 0 and lim f(x) = 3, lim f (x) might still be defined.
x-a+
(c) If lim f(x) = f(a), then the graph of y = f (x) is continuous at x = a.
%3D

Image Transcription

Recall that we say that lim f (x) = L if the (output) values, f(x), of ƒ get arbitrarily close to L as its input values approach a. “Arbitrarily close" means "as close as anyone might ever mandate", very loosely speaking. Please label the following statements as being true or false. Make sure you support your answer with a sketch. (a) If a is not in the domain of f , then lim f(x) is undefined. (b) If lim f() = 0 and lim f(x) = 3, lim f (x) might still be defined. x-a+ (c) If lim f(x) = f(a), then the graph of y = f (x) is continuous at x = a. %3D

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MathCalculus

Continuity

Limits