Question

Which of these limits evaluate to 0?

Answer 1

Answer: C) I and II only

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Work Shown:

Part I

`\displaystyle \lim_(x \to 2)(x-2)/(x+2) = (2-2)/(2+2)\\\\\\\displaystyle \lim_(x \to 2)(x-2)/(x+2) = (0)/(4)\\\\\\\displaystyle \lim_(x \to 2)(x-2)/(x+2) = 0\\\\\\`

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Part II

`\displaystyle \lim_(x \to 0)(\sin(x))/(x+2) = (\sin(0))/(0+2)\\\\\\\displaystyle \lim_(x \to 0)(\sin(x))/(x+2) = (0)/(2)\\\\\\\displaystyle \lim_(x \to 0)(\sin(x))/(x+2) = 0\\\\\\`

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Part III

`\displaystyle \lim_(x \to 5)(x)/(x) = \lim_(x \to 5)1\\\\\\\displaystyle \lim_(x \to 5)(x)/(x) = 1\\\\\\`