Limits of Functions

Limits Warmup


limxx2\lim_{x \to \infty}x^2

If the values of xx increase without bound, what do the values of x2x^2 approach?

A=limx3x9A = \lim_{x \to 3}x-9

B=limx3x29B = \lim_{x \to 3}x^2-9

C=limx3x39C = \lim_{x \to 3}x^3-9

Which limit is equal to 0?0?

A=limx01xA = \lim_{x \to 0}\frac{1}{x}

B=limx0xxB = \lim_{x \to 0}\frac{x}{x}

C=limx0x2xC = \lim_{x \to 0}\frac{x^2}{x}

Which limit is equal to 0?0?

limx0x3xm=1\lim_{x \to 0}\frac{x^3}{x^m} = 1

What must be true of mm?

limx5x210x+25(x5)2\lim_{x \to 5}\frac{x^2-10x+25}{\left(x-5\right)^2}

If the value of xx approaches 5, what does the value of x210x+25(x5)2\frac{x^2-10x+25}{\left(x-5\right)^2} approach?


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