Calculus

Limits of Functions

Limit Misconceptions

         

Evaluate limx51.\lim_{x\to 5} 1.

True or False?

limx01x=.\lim_{x\to 0} \frac{1}{x} = \infty.

Suppose f(x)f(x) is a function defined on the real numbers and limxaf(x)=L.\lim_{x\to a} f(x) = L. Which of the following must be true?

Suppose limxf(x)= and limxg(x)=,\lim_{x\to \infty} f(x) = \infty \text{ and } \lim_{x\to \infty} g(x) = \infty,

and

L=limx(f(x)g(x)).L = \lim_{x\to \infty} (f(x) - g(x)).

Is it possible that L=0L = 0?

Suppose limxf(x)= and limxg(x)=,\lim_{x\to \infty} f(x) = \infty \text{ and } \lim_{x\to \infty} g(x) = \infty,

and

L=limx(f(x)g(x)).L = \lim_{x\to \infty} (f(x) - g(x)).

Is it possible that L=L = -\infty?

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