Limits and Continuity (VCE SSCE Mathematical Methods): Quizzes

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Limits and Continuity
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What does limxaf(x)=p\lim_{x \to a} f(x) = p mean?

f(x)f(x) approaches pp as xx approaches aa

Find limx23x2\lim_{x \to 2} 3x^2.

1212

What is limx3x23xx3\lim_{x \to 3} \frac{x^2 - 3x}{x - 3}?

33

Can a limit exist at x=ax = a if f(a)f(a) is not defined?

Yes, limit describes behavior near a point

For limxaf(x)g(x)\lim_{x \to a} \frac{f(x)}{g(x)}, what restriction applies?

limxag(x)0\lim_{x \to a} g(x) \neq 0

What does limxa+f(x)\lim_{x \to a^+} f(x) represent?

Approaching aa from values greater than aa

When does limxaf(x)\lim_{x \to a} f(x) exist?

When left and right limits exist and equal

For continuity at x=ax = a, what must be true?

f(a)f(a) defined AND limxaf(x)=f(a)\lim_{x \to a} f(x) = f(a)

Which type of functions are continuous everywhere?

All polynomial functions

If f(1)=3f(1) = 3 but limx1f(x)=2\lim_{x \to 1} f(x) = 2, what occurs at x=1x = 1?

Discontinuity

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