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Limits of Functions

When Limits Don't Exist


The graph of y=f(x)y = f(x) is pictured above. For which values of aa in {0,1,2}\{0, 1, 2\} does limxaf(x)\lim_{x \to a} f(x) exist?

Based on the graphs, which limit diverges to \infty as x0?x \to 0?

limxa1x2= a (finite) number\lim_{x \to a} \frac{1}{x^2} = \text{ a (finite) number}

For which choice of aa is the above statement true?

Which option is true of A=limxsin(x)?A = \lim_{x \to \infty} \sin\left(x\right)?

A=limx0xx,B=limx0xxA = \lim_{x \to 0} \frac{x}{x}, \,\,\,\,\,B = \lim_{x \to 0} \frac{|x|}{x}

Which limit(s) exist(s)?


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