3 years ago

What is the first term of the sequence defined by an = 3(n-3) ?

1 answer:

5 0

It’s not that hard. I’m sure you can do it. I’ll be praying for you.

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GarryVolchara [31]

Rewrite the limit as

$\displaystyle\lim_{x\to0}x^2\log x^2=\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}$

Then both numerator and denominator approach infinity (with different signs, but that's not important). Applying L'Hopital's rule, we get

$\displaystyle\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}=\lim_{x\to0}\frac{\frac2x}{-\frac2{x^3}}=\lim_{x\to0}-x^2=\boxed{0}$

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3 years ago