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## Homework Statement:

- $$\lim_{x\to\infty} (x^3 +x^2 +\frac{x}{2})e^{\frac{1}{x}} - \sqrt{x^6+1}$$

## Homework Equations:

- $$e^{\frac{1}{x}}=1, x\xrightarrow{}\infty$$

$$\lim_{x\to\infty} (x^3+x^2 +\frac{x}{2})-x^3\sqrt{(1-\frac{1}{x^6})} = \lim_{x\to\infty} x^3+x^2+ \frac{x}{2} -x^3=\lim_{x\to\infty} x^2 + \frac{x}{2} = \infty. $$

is this it?

is this it?