Calculus

Calculus Level 2

lim ⁡ x → 1 1 − x 2 x 4 − x − 0.16 \lim_{x\to1} \dfrac{1-x^2}{x^4 - x} - 0.16

Find the value of the expression above to 2 decimal places.


The answer is -0.83.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Trevor Arashiro
Aug 7, 2014

We start by rearranging the equation to lim ⁡ x → 1 − x 2 − 1 x ( x 3 − 1 ) ⇒ − ( x − 1 ) ( x + 1 ) x ( x − 1 ) ( x 2 + x + 1 ) → − x + 1 x ( x 2 + x + 1 ) \displaystyle\lim_{x\rightarrow1}-\frac{x^2-1}{x(x^3-1)} \Rightarrow -\frac{(x-1)(x+1)}{x(x-1)(x^2+x+1)} \rightarrow -\frac{x+1}{x(x^2+x+1)} . Now, plugging in 1 for x we get − 2 3 -\dfrac{2}{3} . Now all we have to do is add -.16 and we are left with -0.83

And that "add -.16" really messed me up cuz it really should say "subtract .16".

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