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# f(x)=a(x^{2}) −8x lim f(x)=-1 xrightarrow2 # f(x)=a(x^{2}) −8x lim f(x)=-1 xrightarrow2

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Functions asked 2021-01-13
$$\displaystyle{f{{\left({x}\right)}}}={a}{\left({x}^{{{2}}}\right)}−{8}{x}$$
$$\displaystyle\lim{f{{\left({x}\right)}}}=-{1}$$
$$\displaystyle{x}\rightarrow{2}$$

## Answers (1) 2021-01-14

$$\displaystyle\lim{f{{\left({x}\right)}}}=-{1}$$ Given $$\displaystyle{x}\rightarrow{2}$$
$$\displaystyle\lim{a}{x}^{{{2}}}-{8}{x}=-{1}$$ Substitute $$f(x)=ax^{2}-8x$$ $$\displaystyle{x}\rightarrow{2}$$
$$\displaystyle{a}{2}^{{{2}}}−{8}{\left({2}\right)}=-{1}$$ Evaluate the limit by substituting $$x=2$$.
$$\displaystyle{4}{a}-{16}=-{1}$$ Simplify.
$$\displaystyle{4}{a}={15}$$ Add 16 on both sides.
$$\displaystyle{a}={\frac{{{15}}}{{{4}}}}$$ Divide both sides by 4.

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