a)

$\underset{x\to \infty }{\lim }\left(100+x-x^3\right)=\underset{x\to \infty }{\lim }{x}^3\left(\frac{100}{x^3}+\frac{1}{x^2}-1\right)=$  

$=\infty \cdot \left(0+0-1\right)=\infty \cdot \left(-1\right)=-\infty$  

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b) 

$\underset{x\to -\infty }{\lim }\left(\frac{x^4}{10}+2x^3+x^2\right)=\underset{x\to -\infty }{\lim }{x}^4\left(\frac{1}{10}+\frac{2}{x}+\frac{1}{x^2}\right)=$  

$=\infty \cdot \left(\frac{1}{10}+0+0\right)=\infty \cdot \frac{1}{10}=\infty$  

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c)

$\underset{x\to -\infty }{\lim }{\left(x^3+x\right)}^3=\underset{x\to -\infty }{\lim }{\left(x^3\left(1+\frac{1}{x^2}\right)\right)}^3=$  

$=\underset{x\to -\infty }{\lim }{x}^9{\left(1+\frac{1}{x^2}\right)}^3=-\infty \cdot {\left(1+0\right)}^3=$  

$=-\infty \cdot 1=-\infty$