Calculus Examples

$lim_{x \to \infty} - 1 + x^{2} - x^{3} + 3 x^{4}$

Step 1

Simplify the expression.

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Step 1.1

Reorder $- 1$ and $x^{2}$ .

$lim_{x \to \infty} x^{2} - 1 - x^{3} + 3 x^{4}$

Step 1.2

Move $- 1$ .

$lim_{x \to \infty} x^{2} - x^{3} - 1 + 3 x^{4}$

Step 1.3

Reorder $x^{2}$ and $- x^{3}$ .

$lim_{x \to \infty} - x^{3} + x^{2} - 1 + 3 x^{4}$

Step 1.4

Move $- 1$ .

$lim_{x \to \infty} - x^{3} + x^{2} + 3 x^{4} - 1$

Step 1.5

Move $x^{2}$ .

$lim_{x \to \infty} - x^{3} + 3 x^{4} + x^{2} - 1$

Step 1.6

Reorder $- x^{3}$ and $3 x^{4}$ .

$lim_{x \to \infty} 3 x^{4} - x^{3} + x^{2} - 1$

Step 2

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

$\infty$