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$$\lim _{x\to 1} \frac{x^3 +x-2}{1-x}$$ can you please tell how to solve this ?! I tried too many things, non worked ! it is not zero for sure ! mathway gave me $-4$ (no steps)

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closed as off-topic by AlexR, Hayden, Claude Leibovici, Mathmo123, Giuseppe Negro Jul 22 at 11:28

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Welcome to math.SE! This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level. –  user37238 Jul 22 at 10:27
    
What methods have you tried? –  Rainier van Es Jul 22 at 10:32
    
note that given $P(x)=x^3+x-2$, that $P(1)=0$, so 1 is a root of $P$, and therefore, $x-1$ is a factor. –  John Joy Jul 22 at 16:29

2 Answers 2

HINT:

$$x^3+x-2=x^3-1+x-1=(x-1)(x^2+x+1)+(x-1)$$

Use $\displaystyle x\to1\implies x\ne1\iff x-1\ne0$

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hopital rule will give you

$$\lim _{x\to 1} \frac{3x^2 +1}{-1}=-4$$

L'Hôpital's rule

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