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Vladimir79 [104]
3 years ago
11

Which set of ordered pairs represents a function?

Mathematics
1 answer:
alekssr [168]3 years ago
6 0

Answer: {(-6, -6), (-2,-2), (7,-6),(-5,0)}

Step-by-step explanation:

To find the ordered pairs that represent a function, we want to find one that doesn't have multiple outputs for one input.

{(-6, -6), (-2,-2), (7,-6),(-5,0)} is the correct answer because all the x are different, and have only one output.

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Given:

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Solve:

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Use l'hopital's rule:

\begin{gathered} =\lim _{x\to0}\frac{\frac{d}{dx}(-\sin 2x+\tan 2x)}{\frac{d}{dx}(x^3)} \\ =\lim _{x\to0}\frac{-2\cos (2x)+2\tan ^2(2x)+2}{3x^2} \end{gathered}

Simplify:

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Apply the constant multiple rule:

\begin{gathered} \lim _{x\to0}cf(x)=c\lim _{x\to0}f(x) \\ \text{With c=}\frac{2}{3} \\ f(x)=\frac{-\cos (2x)+\tan ^2(2x)+1}{x^2} \end{gathered}\begin{gathered} =\frac{2\lim _{x\to0}\frac{-\cos (2x)+\tan ^2(2x)+1}{x^2}}{3} \\ =\frac{2\lim _{x\rightarrow0}\frac{(4\tan ^2(2x)+4)\tan (2x)+2\sin (2x)}{2x}}{3} \end{gathered}

Similary :

\begin{gathered} =\frac{2\lim _{x\to0}(2\cos (2x)+12\tan ^4(2x)+16\tan ^2(2x)+4)}{3} \\ =\frac{2(6)}{3} \\ =4 \end{gathered}

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