Calculus Examples

$lim_{x \to - \infty} \frac{4 x^{7}}{2 x^{3}}$

Step 1

Reduce.

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Step 1.1

Cancel the common factor of $4$ and $2$ .

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Step 1.1.1

Factor $2$ out of $4 x^{7}$ .

$lim_{x \to - \infty} \frac{2 (2 x^{7})}{2 x^{3}}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $2 x^{3}$ .

$lim_{x \to - \infty} \frac{2 (2 x^{7})}{2 (x^{3})}$

Step 1.1.2.2

Cancel the common factor.

$lim_{x \to - \infty} \frac{2 (2 x^{7})}{2 x^{3}}$

Step 1.1.2.3

Rewrite the expression.

$lim_{x \to - \infty} \frac{2 x^{7}}{x^{3}}$

Step 1.2

Cancel the common factor of $x^{7}$ and $x^{3}$ .

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Step 1.2.1

Factor $x^{3}$ out of $2 x^{7}$ .

$lim_{x \to - \infty} \frac{x^{3} (2 x^{4})}{x^{3}}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Multiply by $1$ .

$lim_{x \to - \infty} \frac{x^{3} (2 x^{4})}{x^{3} \cdot 1}$

Step 1.2.2.2

Cancel the common factor.

$lim_{x \to - \infty} \frac{x^{3} (2 x^{4})}{x^{3} \cdot 1}$

Step 1.2.2.3

Rewrite the expression.

$lim_{x \to - \infty} \frac{2 x^{4}}{1}$

Step 1.2.2.4

Divide $2 x^{4}$ by $1$ .

$lim_{x \to - \infty} 2 x^{4}$

Step 2

The limit at negative infinity of a polynomial of even degree whose leading coefficient is positive is infinity.

$\infty$